Alexander Bonilla
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Alexander Bonilla has a total of 291 co-authors. Here are the top co-authors by number of shared publications:
- Rafael C. Nunes
Universidade Federal do Rio Grande do Sul
10 shared publications - Everton M. C. Abreu
Universidade Federal Rural do Rio de Janeiro
5 shared publications - Suresh Kumar
Plaksha University
4 shared publications - Jairo Ernesto Castillo Hernandez
Universidad Distrital Francisco José de Caldas, FIZMAKO Research Group, Bogotá, Colombia
3 shared publications - Jeremy M. Wachter
Wentworth Institute of Technology
3 shared publications - Jorge Ananias Neto
Universidade Federal de Juiz de Fora
3 shared publications
Latest Publications
- Open Access
- 31 July 2026
- Published by American Astronomical Society in The Astrophysical Journal Letters
- Vol. 1006 (2) , L67
Erratum: “The NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background” (2023, ApJL, 952, L37)
In the published article, we presented inferences about the population of supermassive black hole (SMBH) binaries emitting at nanohertz gravitational-wave (GW) frequencies based on the 15 yr dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). Here, we report two bugs in the astrophysical analysis software used for the published article. While parameter posteriors of our inference can be seen to have slight differences on close inspection, none of the conclusions from the original publication have changed, including the finding that the measured GW background is dominated by the most massive, high-mass-ratio SMBH binaries. Our corrected results show slightly less evidence for environmental interactions with SMBH binaries and indicate that the population of SMBH binaries contributing to the GW background occurs at slightly higher mass ratios and redshifts than indicated in the published article. Correcting these errors does not change the central conclusion that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency GW spectrum. These errors did not affect any other analyses of the NANOGrav 15 yr dataset, including the evidence for a GW background presented in another of our published articles.
- 31 July 2026
- Published by American Astronomical Society in The Astrophysical Journal Letters
- Vol. 1006 (2) , L67
Open AccessErratum: “The NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background” (2023, ApJL, 952, L37)
In the published article, we presented inferences about the population of supermassive black hole (SMBH) binaries emitting at nanohertz gravitational-wave (GW) frequencies based on the 15 yr dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). Here, we report two bugs in the astrophysical analysis software used for the published article. While parameter posteriors of our inference can be seen to have slight differences on close inspection, none of the conclusions from the original publication have changed, including the finding that the measured GW background is dominated by the most massive, high-mass-ratio SMBH binaries. Our corrected results show slightly less evidence for environmental interactions with SMBH binaries and indicate that the population of SMBH binaries contributing to the GW background occurs at slightly higher mass ratios and redshifts than indicated in the published article. Correcting these errors does not change the central conclusion that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency GW spectrum. These errors did not affect any other analyses of the NANOGrav 15 yr dataset, including the evidence for a GW background presented in another of our published articles.
- Top Cited PapersOpen Access
- 30 October 2025
- Published by Springer Nature in Living Reviews in Relativity
- Vol. 28 (1)
Waveform modelling for the Laser Interferometer Space Antenna
LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.
- 30 October 2025
- Published by Springer Nature in Living Reviews in Relativity
- Vol. 28 (1)
Top Cited PapersOpen AccessWaveform modelling for the Laser Interferometer Space Antenna
LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.
- Open Access
Revisiting the temperature evolution law of the CMB with gaussian processes
In this work, we perform a statistical inference of the classical background law governing the evolution of the temperature of the cosmic microwave background radiation (CMB), given by $T_{\rm CMB}(z) = T_0(1 + z)$. To this end, we employ Gaussian Process (GP) regression techniques to reconstruct the temperature evolution based on two observational datasets: (i) CMB-Sunyaev-Zel'dovich (SZ) cluster measurements and (ii) CMB-interstellar medium (ISM) interaction data. Our analysis reveals interesting results that may suggest potential deviations from the standard temperature-redshift relation, particularly at low redshifts ($z < 0.5$), where discrepancies up to $\sim$2$\sigma$ are observed. Additionally, we identify a mild but noteworthy tension, also at the $\sim$2$\sigma$ level, between our GP inferred value of the present-day CMB temperature, $T_{\rm CMB}(z=0)$, and the precise direct measurement from the COBE/FIRAS experiment. We also explore possible phenomenological implications of our findings, including interpretations associated with possible variations in fundamental constants, such as the fine-structure constant $\alpha$, which could provide a physical explanation for the observed deviations at low redshift.Open AccessRevisiting the temperature evolution law of the CMB with gaussian processes
In this work, we perform a statistical inference of the classical background law governing the evolution of the temperature of the cosmic microwave background radiation (CMB), given by $T_{\rm CMB}(z) = T_0(1 + z)$. To this end, we employ Gaussian Process (GP) regression techniques to reconstruct the temperature evolution based on two observational datasets: (i) CMB-Sunyaev-Zel'dovich (SZ) cluster measurements and (ii) CMB-interstellar medium (ISM) interaction data. Our analysis reveals interesting results that may suggest potential deviations from the standard temperature-redshift relation, particularly at low redshifts ($z < 0.5$), where discrepancies up to $\sim$2$\sigma$ are observed. Additionally, we identify a mild but noteworthy tension, also at the $\sim$2$\sigma$ level, between our GP inferred value of the present-day CMB temperature, $T_{\rm CMB}(z=0)$, and the precise direct measurement from the COBE/FIRAS experiment. We also explore possible phenomenological implications of our findings, including interpretations associated with possible variations in fundamental constants, such as the fine-structure constant $\alpha$, which could provide a physical explanation for the observed deviations at low redshift. - Open Access
- 13 March 2025
- Published by Elsevier in Physics Letters B
- Vol. 864
VSL-Gravity in light of PSR B1913+16 full data set: Upper limits on graviton mass and its theoretical consequences
- 13 March 2025
- Published by Elsevier in Physics Letters B
- Vol. 864
Open AccessVSL-Gravity in light of PSR B1913+16 full data set: Upper limits on graviton mass and its theoretical consequences
- Open Access
- 25 June 2024
- Published by Springer Nature in The European Physical Journal C
- Vol. 84 (6) , 1-11
Reconstructing the growth index $\gamma $ with Gaussian processesAlternative cosmological models have been proposed to alleviate the tensions reported in the concordance cosmological model, or to explain the current accelerated phase of the universe. One way to distinguish between General Relativity and modified gravity models is using current astronomical data to measure the growth index $$\gamma $$ , a parameter related to the growth of matter perturbations, which behaves differently in different metric theories. We propose a model independent methodology for determining $$\gamma $$ , where our analyses combine diverse cosmological data sets, namely $$\{ f(z_i) \}$$ , $$\{ [f\sigma _8](z_i) \}$$ , and $$\{ H(z_i) \}$$ , and use Gaussian Processes, a non-parametric approach suitable to reconstruct functions. This methodology is a new consistency test for $$\gamma $$ constant. Our results show that, for the redshift interval $$0< z < 1$$ , $$\gamma $$ is consistent with the constant value $$\gamma = 0.55$$ , expected in General Relativity theory, within $$2 \sigma $$ confidence level (CL). Moreover, we find $$\gamma (z=0)$$ = 0.311 $$\pm 0.144 $$ and $$\gamma (z=0) = 0.609 \pm 0.200$$ for the reconstructions using the $$\{ f(z_i) \}$$ and $$\{ [f\sigma _8](z_i) \}$$ data sets, respectively, values that also agree at a 2 $$\sigma $$ CL with $$\gamma = 0.55$$ . Our methodology and analyses can be considered as an alternative approach in light of the current discussion in the literature that suggests a possible evidence for the growth index evolution.- 25 June 2024
- Published by Springer Nature in The European Physical Journal C
- Vol. 84 (6) , 1-11
Open AccessReconstructing the growth index $\gamma $ with Gaussian processesAlternative cosmological models have been proposed to alleviate the tensions reported in the concordance cosmological model, or to explain the current accelerated phase of the universe. One way to distinguish between General Relativity and modified gravity models is using current astronomical data to measure the growth index $$\gamma $$ , a parameter related to the growth of matter perturbations, which behaves differently in different metric theories. We propose a model independent methodology for determining $$\gamma $$ , where our analyses combine diverse cosmological data sets, namely $$\{ f(z_i) \}$$ , $$\{ [f\sigma _8](z_i) \}$$ , and $$\{ H(z_i) \}$$ , and use Gaussian Processes, a non-parametric approach suitable to reconstruct functions. This methodology is a new consistency test for $$\gamma $$ constant. Our results show that, for the redshift interval $$0< z < 1$$ , $$\gamma $$ is consistent with the constant value $$\gamma = 0.55$$ , expected in General Relativity theory, within $$2 \sigma $$ confidence level (CL). Moreover, we find $$\gamma (z=0)$$ = 0.311 $$\pm 0.144 $$ and $$\gamma (z=0) = 0.609 \pm 0.200$$ for the reconstructions using the $$\{ f(z_i) \}$$ and $$\{ [f\sigma _8](z_i) \}$$ data sets, respectively, values that also agree at a 2 $$\sigma $$ CL with $$\gamma = 0.55$$ . Our methodology and analyses can be considered as an alternative approach in light of the current discussion in the literature that suggests a possible evidence for the growth index evolution. - Top Cited PapersOpen Access
- 1 August 2023
- Published by American Astronomical Society in The Astrophysical Journal Letters
- Vol. 952 (2) , L37
The NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background
The NANOGrav 15 yr data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15 yr observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach subparsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations.
- 1 August 2023
- Published by American Astronomical Society in The Astrophysical Journal Letters
- Vol. 952 (2) , L37
Top Cited PapersOpen AccessThe NANOGrav 15 yr Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational-wave Background
The NANOGrav 15 yr data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15 yr observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach subparsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations.
- Open Access
Reconstruction of the dark sectors' interaction: A model-independent inference and forecast from GW standard sirens
Interacting dark matter (DM) - dark energy (DE) models have been intensively investigated in the literature for their ability to fit various data sets as well as to explain some observational tensions persisting within the $\Lambda$CDM cosmology. In this work, we employ the Gaussian processes (GP) algorithm to perform a joint analysis by using the geometrical cosmological probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the coupling function between the dark components in a general framework, where the DE can assume a dynamical character via its equation of state. In addition to the joint analysis with these data, we simulate a catalogue with standard siren events from binary neutron star mergers, within the sensitivity predicted by the Einstein Telescope, to reconstruct the dark sector coupling with more accuracy in a robust way. We find that the particular case, where $w = -1$ is fixed on the DE nature, has a statistical preference for an interaction in the dark sector at late times. In the general case, where $w(z)$ is analysed, we find no evidence for such dark coupling, and the predictions are compatible with the $\Lambda$CDM paradigm. When the mock events of the standard sirens are considered to improve the kernel in GP predictions, we find a preference for an interaction in the dark sector at late times.Open AccessReconstruction of the dark sectors' interaction: A model-independent inference and forecast from GW standard sirens
Interacting dark matter (DM) - dark energy (DE) models have been intensively investigated in the literature for their ability to fit various data sets as well as to explain some observational tensions persisting within the $\Lambda$CDM cosmology. In this work, we employ the Gaussian processes (GP) algorithm to perform a joint analysis by using the geometrical cosmological probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the coupling function between the dark components in a general framework, where the DE can assume a dynamical character via its equation of state. In addition to the joint analysis with these data, we simulate a catalogue with standard siren events from binary neutron star mergers, within the sensitivity predicted by the Einstein Telescope, to reconstruct the dark sector coupling with more accuracy in a robust way. We find that the particular case, where $w = -1$ is fixed on the DE nature, has a statistical preference for an interaction in the dark sector at late times. In the general case, where $w(z)$ is analysed, we find no evidence for such dark coupling, and the predictions are compatible with the $\Lambda$CDM paradigm. When the mock events of the standard sirens are considered to improve the kernel in GP predictions, we find a preference for an interaction in the dark sector at late times. - 12 March 2022
- Published by Oxford University Press (OUP) in Monthly Notices of the Royal Astronomical Society
- Vol. 512 (3) , 4231-4238
Reconstruction of the dark sectors’ interaction: A model-independent inference and forecast from GW standard sirens
Interacting dark matter (DM) – dark energy (DE) models have been intensively investigated in the literature for their ability to fit various data sets as well as to explain some observational tensions persisting within the ΛCDM cosmology. In this work, we employ the Gaussian processes (GP) algorithm to perform a joint analysis by using the geometrical cosmological probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the coupling function between the dark components in a general framework, where the DE can assume a dynamical character via its equation of state. In addition to the joint analysis with these data, we simulate a catalogue with standard siren events from binary neutron star mergers, within the sensitivity predicted by the Einstein Telescope, to reconstruct the dark sector coupling with more accuracy in a robust way. We find that the particular case, where w = −1 is fixed on the DE nature, has a statistical preference for an interaction in the dark sector at late times. In the general case, where w(z) is analysed, we find no evidence for such dark coupling, and the predictions are compatible with the ΛCDM paradigm. When the mock events of the standard sirens are considered to improve the kernel in GP predictions, we find a preference for an interaction in the dark sector at late times.
- 12 March 2022
- Published by Oxford University Press (OUP) in Monthly Notices of the Royal Astronomical Society
- Vol. 512 (3) , 4231-4238
Reconstruction of the dark sectors’ interaction: A model-independent inference and forecast from GW standard sirens
Interacting dark matter (DM) – dark energy (DE) models have been intensively investigated in the literature for their ability to fit various data sets as well as to explain some observational tensions persisting within the ΛCDM cosmology. In this work, we employ the Gaussian processes (GP) algorithm to perform a joint analysis by using the geometrical cosmological probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the coupling function between the dark components in a general framework, where the DE can assume a dynamical character via its equation of state. In addition to the joint analysis with these data, we simulate a catalogue with standard siren events from binary neutron star mergers, within the sensitivity predicted by the Einstein Telescope, to reconstruct the dark sector coupling with more accuracy in a robust way. We find that the particular case, where w = −1 is fixed on the DE nature, has a statistical preference for an interaction in the dark sector at late times. In the general case, where w(z) is analysed, we find no evidence for such dark coupling, and the predictions are compatible with the ΛCDM paradigm. When the mock events of the standard sirens are considered to improve the kernel in GP predictions, we find a preference for an interaction in the dark sector at late times.
- Open AccessMeasurements of $H_0$ and reconstruction of the dark energy properties from a model-independent joint analysisGaussian processes (GP) provide an elegant and model-independent method for extracting cosmological information from the observational data. In this work, we employ GP to perform a joint analysis by using the geometrical cosmological probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the Hubble constant $H_0$, and reconstruct some properties of dark energy (DE), viz., the equation of state parameter $w$, the sound speed of DE perturbations $c^2_s$, and the ratio of DE density evolution $X = \rho_{\rm de}/\rho_{\rm de,0}$. From the joint analysis SN+CC+BAO+H0LiCOW, we find that $H_0$ is constrained at 1.1\% precision with $H_0 = 73.78 \pm 0.84$ km s$^{-1}$Mpc$^{-1}$, which is in agreement with SH0ES and H0LiCOW estimates, but in $\sim$6.2$\sigma$ tension with the current CMB measurements of $H_0$. With regard to the DE parameters, we find $c^2_s < 0$ at $\sim$2$\sigma$ at high $z$, and the possibility of $X$ to become negative for $z > 1.5$. We compare our results with the ones obtained in the literature, and discuss the consequences of our main results on the DE theoretical framework.Open AccessMeasurements of $H_0$ and reconstruction of the dark energy properties from a model-independent joint analysisGaussian processes (GP) provide an elegant and model-independent method for extracting cosmological information from the observational data. In this work, we employ GP to perform a joint analysis by using the geometrical cosmological probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the Hubble constant $H_0$, and reconstruct some properties of dark energy (DE), viz., the equation of state parameter $w$, the sound speed of DE perturbations $c^2_s$, and the ratio of DE density evolution $X = \rho_{\rm de}/\rho_{\rm de,0}$. From the joint analysis SN+CC+BAO+H0LiCOW, we find that $H_0$ is constrained at 1.1\% precision with $H_0 = 73.78 \pm 0.84$ km s$^{-1}$Mpc$^{-1}$, which is in agreement with SH0ES and H0LiCOW estimates, but in $\sim$6.2$\sigma$ tension with the current CMB measurements of $H_0$. With regard to the DE parameters, we find $c^2_s < 0$ at $\sim$2$\sigma$ at high $z$, and the possibility of $X$ to become negative for $z > 1.5$. We compare our results with the ones obtained in the literature, and discuss the consequences of our main results on the DE theoretical framework.
- Open Access
- 5 February 2021
- Published by Springer Nature in The European Physical Journal C
- Vol. 81 (2) , 1-13
Measurements of $H_0$ and reconstruction of the dark energy properties from a model-independent joint analysisGaussian processes (GP) provide an elegant and model-independent method for extracting cosmological information from the observational data. In this work, we employ GP to perform a joint analysis by using the geometrical cosmological probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the Hubble constant $$H_0$$ , and reconstruct some properties of dark energy (DE), viz., the equation of state parameter w, the sound speed of DE perturbations $$c^2_s$$ , and the ratio of DE density evolution $$X = \rho _\mathrm{de}/\rho _\mathrm{de,0}$$ . From the joint analysis SN+CC+BAO+H0LiCOW, we find that $$H_0$$ is constrained at 1.1% precision with $$H_0 = 73.78 \pm 0.84\ \hbox {km}\ \hbox {s}^{-1}\,\hbox {Mpc}^{-1}$$ , which is in agreement with SH0ES and H0LiCOW estimates, but in $$\sim 6.2 \sigma $$ tension with the current CMB measurements of $$H_0$$ . With regard to the DE parameters, we find $$c^2_s < 0$$ at $$\sim 2 \sigma $$ at high z, and the possibility of X to become negative for $$z > 1.5$$ . We compare our results with the ones obtained in the literature, and discuss the consequences of our main results on the DE theoretical framework.- 5 February 2021
- Published by Springer Nature in The European Physical Journal C
- Vol. 81 (2) , 1-13
Open AccessMeasurements of $H_0$ and reconstruction of the dark energy properties from a model-independent joint analysisGaussian processes (GP) provide an elegant and model-independent method for extracting cosmological information from the observational data. In this work, we employ GP to perform a joint analysis by using the geometrical cosmological probes such as Supernova Type Ia (SN), Cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the H0LiCOW lenses sample to constrain the Hubble constant $$H_0$$ , and reconstruct some properties of dark energy (DE), viz., the equation of state parameter w, the sound speed of DE perturbations $$c^2_s$$ , and the ratio of DE density evolution $$X = \rho _\mathrm{de}/\rho _\mathrm{de,0}$$ . From the joint analysis SN+CC+BAO+H0LiCOW, we find that $$H_0$$ is constrained at 1.1% precision with $$H_0 = 73.78 \pm 0.84\ \hbox {km}\ \hbox {s}^{-1}\,\hbox {Mpc}^{-1}$$ , which is in agreement with SH0ES and H0LiCOW estimates, but in $$\sim 6.2 \sigma $$ tension with the current CMB measurements of $$H_0$$ . With regard to the DE parameters, we find $$c^2_s < 0$$ at $$\sim 2 \sigma $$ at high z, and the possibility of X to become negative for $$z > 1.5$$ . We compare our results with the ones obtained in the literature, and discuss the consequences of our main results on the DE theoretical framework.