Deepak Jain
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Deepak Jain has a total of 39 co-authors. Here are the top co-authors by number of shared publications:
- Amitabha Mukherjee
Department of Physics and Astrophysics University of Delhi 110007 Delhi India
8 shared publications - Rodrigo F. L. Holanda
Departamento de Física Teórica e Experimental Universidade Federal do Rio Grande do Norte 59300-000 Natal -RN Brazil
8 shared publications - Shobhit Mahajan
Department of Physics and Astrophysics University of Delhi 110007 Delhi India
7 shared publications - Shobhit Mahajan
Department of Physics and Astrophysics University of Delhi 110007 Delhi India
6 shared publications - Darshan Kumar
Henan Academy of Sciences
5 shared publications Remya Nair
Centre for Theoretical Physics Jamia Millia Islamia 110025 New Delhi India
5 shared publications
Latest Publications
- Open Access
A cosmographic analysis using DESI-DR2 and strong lensing: II. Distance Ratio measurements
The distance ratio derived from strong gravitational lensing systems, combined with complementary cosmological observations, offers a model-independent means to investigate the geometry and dynamics of the universe. In this study, we carry out a cosmographic investigation using the latest compilations of Type Ia supernovae (PantheonPlus, DESY5, and Union3), baryon acoustic oscillation measurements from DESI-DR2, and updated strong lensing distance ratios. The cosmographic series is expanded to fourth order in the variable $y = z/(1+z)$ to constrain the deceleration, jerk, and snap parameters $(q_0,~j_0,~s_0)$. The analysis utilizes the distance sum rule (DSR) to provide an independent assessment of the spatial curvature parameter, $Ω_{k0}$, without assuming a specific dynamical model. Our results based on SGL distance ratio measurements combined with individual supernova datasets suggest a mild preference for an open universe, though a flat universe is supported at the 95% confidence level. Further, the inclusion of DESI-DR2 data in each combination provides tighter constraints on the parameters and confirms flatness within the 68% confidence level as expected in standard cosmology. The results for $q_0$ and $j_0$ are consistent with $Λ$CDM predictions across datasets, while the constraint on $s_0$ remains limited but improves with the inclusion of DESI-DR2. This is the second and final paper in a two-part series.Open AccessA cosmographic analysis using DESI-DR2 and strong lensing: II. Distance Ratio measurements
The distance ratio derived from strong gravitational lensing systems, combined with complementary cosmological observations, offers a model-independent means to investigate the geometry and dynamics of the universe. In this study, we carry out a cosmographic investigation using the latest compilations of Type Ia supernovae (PantheonPlus, DESY5, and Union3), baryon acoustic oscillation measurements from DESI-DR2, and updated strong lensing distance ratios. The cosmographic series is expanded to fourth order in the variable $y = z/(1+z)$ to constrain the deceleration, jerk, and snap parameters $(q_0,~j_0,~s_0)$. The analysis utilizes the distance sum rule (DSR) to provide an independent assessment of the spatial curvature parameter, $Ω_{k0}$, without assuming a specific dynamical model. Our results based on SGL distance ratio measurements combined with individual supernova datasets suggest a mild preference for an open universe, though a flat universe is supported at the 95% confidence level. Further, the inclusion of DESI-DR2 data in each combination provides tighter constraints on the parameters and confirms flatness within the 68% confidence level as expected in standard cosmology. The results for $q_0$ and $j_0$ are consistent with $Λ$CDM predictions across datasets, while the constraint on $s_0$ remains limited but improves with the inclusion of DESI-DR2. This is the second and final paper in a two-part series. - Open Access
A cosmographic analysis using DESI-DR2 and strong lensing: I. Time-Delay measurements
Strong gravitational lensing time-delay measurements, together with the distance sum rule (DSR), offer a model-independent approach to probe the geometry and expansion of the universe without relying on a fiducial cosmological model. In this work, we perform a cosmographic analysis by combining the latest Type Ia supernova datasets (PantheonPlus, DESY5, and Union3), baryon acoustic oscillation data from DESI-DR2, and updated time-delay distances from strong lensing systems. The analyses using SGL with individual SNIa datasets (SGL+PantheonPlus, SGL+DESY5, and SGL+Union3) indicate a preference for an open universe, though they remain consistent with spatially flat universe at the $95%$ confidence level. When DESI-DR2 data is included in each combination, the constraints tighten and shift slightly toward a closed universe, while flatness remains supported at the $68%$ confidence level. The best-fit values of $q_0$ and $j_0$ agree with $Λ$CDM expectations within $95%$ or $99%$ confidence depending on the dataset, whereas $s_0$ remains weakly constrained in all cases. This work is the first in a series of two companion papers on cosmography with DESI-DR2 and strong lensing.Open AccessA cosmographic analysis using DESI-DR2 and strong lensing: I. Time-Delay measurements
Strong gravitational lensing time-delay measurements, together with the distance sum rule (DSR), offer a model-independent approach to probe the geometry and expansion of the universe without relying on a fiducial cosmological model. In this work, we perform a cosmographic analysis by combining the latest Type Ia supernova datasets (PantheonPlus, DESY5, and Union3), baryon acoustic oscillation data from DESI-DR2, and updated time-delay distances from strong lensing systems. The analyses using SGL with individual SNIa datasets (SGL+PantheonPlus, SGL+DESY5, and SGL+Union3) indicate a preference for an open universe, though they remain consistent with spatially flat universe at the $95%$ confidence level. When DESI-DR2 data is included in each combination, the constraints tighten and shift slightly toward a closed universe, while flatness remains supported at the $68%$ confidence level. The best-fit values of $q_0$ and $j_0$ agree with $Λ$CDM expectations within $95%$ or $99%$ confidence depending on the dataset, whereas $s_0$ remains weakly constrained in all cases. This work is the first in a series of two companion papers on cosmography with DESI-DR2 and strong lensing. - 1 October 2025
- Published by Springer Nature in Resonance
- Vol. 30 (10) , 1329-1348
Revisiting the Concept of Macrostates and Microstates in a Degenerate System: Finite and Infinite Levels
- 1 October 2025
- Published by Springer Nature in Resonance
- Vol. 30 (10) , 1329-1348
Revisiting the Concept of Macrostates and Microstates in a Degenerate System: Finite and Infinite Levels
- 1 March 2024
- Published by Springer Nature in Resonance
- Vol. 29 (3) , 361-373
Some Positive Thoughts about Negative Absolute Temperature
- 1 March 2024
- Published by Springer Nature in Resonance
- Vol. 29 (3) , 361-373
Some Positive Thoughts about Negative Absolute Temperature
- 26 July 2023
- Published by IOP Publishing in Research in Astronomy and Astrophysics
- Vol. 23 (9) , 095001
Revisiting the Epoch of Cosmic Acceleration
We revisit the epoch of cosmic speed-up characterized by the redshift of transition from a decelerated to an accelerated phase. This redshift is termed the transition redshift (z t ). We use the spatially flat and non-flat variants of the most common ΛCDM and XCDM models to put constraints on the transition redshift along with the other model parameters. The data for this analysis come from the recent and updated Pantheon+ supernova (SN) data set and the Hubble parameter measurements obtained from Cosmic Chronometers. We consider both data sets with their respective covariance matrices incorporating all statistical and systematic uncertainties. We observe that using the combined data sets of H(z) and SNe, the best fit value of transition redshift lies in the range 0.61 < z t < 0.79 for all four dark energy models. Incidentally, we observe a positive curvature for the non-flat models, correlations between several model parameters and a strong degeneracy between the curvature and the equation of state parameter.
- 26 July 2023
- Published by IOP Publishing in Research in Astronomy and Astrophysics
- Vol. 23 (9) , 095001
Revisiting the Epoch of Cosmic Acceleration
We revisit the epoch of cosmic speed-up characterized by the redshift of transition from a decelerated to an accelerated phase. This redshift is termed the transition redshift (z t ). We use the spatially flat and non-flat variants of the most common ΛCDM and XCDM models to put constraints on the transition redshift along with the other model parameters. The data for this analysis come from the recent and updated Pantheon+ supernova (SN) data set and the Hubble parameter measurements obtained from Cosmic Chronometers. We consider both data sets with their respective covariance matrices incorporating all statistical and systematic uncertainties. We observe that using the combined data sets of H(z) and SNe, the best fit value of transition redshift lies in the range 0.61 < z t < 0.79 for all four dark energy models. Incidentally, we observe a positive curvature for the non-flat models, correlations between several model parameters and a strong degeneracy between the curvature and the equation of state parameter.
- Open AccessConstraints on the transition redshift from the calibrated Gamma-ray Burst $E_{\rm p}$-$E_{\rm iso}$ correlationWe constrain the deceleration-acceleration epoch, namely the transition redshift $z_{tr}$, adopting model-independent techniques that utilize a calibrated $E_{\rm p}$-$E_{\rm iso}$ correlation for gamma-ray bursts (GRBs). To do so, in addition to real data points, we employ up to $1000$ simulated observational Hubble data (OHD) points. We then calibrate the $E_{\rm p}$-$E_{\rm iso}$ correlation by means of the well-consolidate B\'ezier polynomial technique, interpolating OHD up to the second order. Once GRB data have been calibrated, we consider two strategies of cosmographic expansions, i.e., first we take a direct Hubble rate expansion around $z_{tr}$, and second the expansion of the deceleration parameter around the same redshift, but with a different order. Employing type Ia supernovae, baryonic acoustic oscillations and GRB data sets, from Monte Carlo analyses we infer tight constraints on $z_{tr}$ and the jerk parameters at $z=z_{tr}$, namely $j_{tr}$. Our results are extremely compatible with previous outcomes and confirm the $\Lambda$CDM predictions, being slightly different in terms of the jerk parameter. In this respect, we conjecture which extensions of the concordance paradigm are possible and we compare our findings with expectations provided by generic dark energy models.Open AccessConstraints on the transition redshift from the calibrated Gamma-ray Burst $E_{\rm p}$-$E_{\rm iso}$ correlationWe constrain the deceleration-acceleration epoch, namely the transition redshift $z_{tr}$, adopting model-independent techniques that utilize a calibrated $E_{\rm p}$-$E_{\rm iso}$ correlation for gamma-ray bursts (GRBs). To do so, in addition to real data points, we employ up to $1000$ simulated observational Hubble data (OHD) points. We then calibrate the $E_{\rm p}$-$E_{\rm iso}$ correlation by means of the well-consolidate B\'ezier polynomial technique, interpolating OHD up to the second order. Once GRB data have been calibrated, we consider two strategies of cosmographic expansions, i.e., first we take a direct Hubble rate expansion around $z_{tr}$, and second the expansion of the deceleration parameter around the same redshift, but with a different order. Employing type Ia supernovae, baryonic acoustic oscillations and GRB data sets, from Monte Carlo analyses we infer tight constraints on $z_{tr}$ and the jerk parameters at $z=z_{tr}$, namely $j_{tr}$. Our results are extremely compatible with previous outcomes and confirm the $\Lambda$CDM predictions, being slightly different in terms of the jerk parameter. In this respect, we conjecture which extensions of the concordance paradigm are possible and we compare our findings with expectations provided by generic dark energy models.
- Open Access
Gamma Rays Bursts: A Viable Cosmological Probe?
In this work, our focus is on exploring the potential of current GRB measurements to provide reliable constraints on cosmological model parameters at high redshift. This work is divided into two parts. First, we calibrate the Amati relation in a model-independent way by using Hubble parameter measurements obtained from the differential ages of the galaxies. We further check if the Amati relation parameters evolve with the GRBs' redshift or not, using the data of Old Astrophysical Objects. The results indicate that GRBs do seem to evolve with redshift. In the second part, we test different cosmological models with the calibrated GRB data obtained by using constant and dynamical Amati relation. Our results indicate that the present quality of GRB data is not good enough to put tight constraints on the cosmological parameters. Hence we perform a joint analysis with the combined data of GRBs and Type Ia Supernovae (SNe) and find that this can considerably enhance cosmological constraints in contrast to solely relying on GRBs.
Open AccessGamma Rays Bursts: A Viable Cosmological Probe?
In this work, our focus is on exploring the potential of current GRB measurements to provide reliable constraints on cosmological model parameters at high redshift. This work is divided into two parts. First, we calibrate the Amati relation in a model-independent way by using Hubble parameter measurements obtained from the differential ages of the galaxies. We further check if the Amati relation parameters evolve with the GRBs' redshift or not, using the data of Old Astrophysical Objects. The results indicate that GRBs do seem to evolve with redshift. In the second part, we test different cosmological models with the calibrated GRB data obtained by using constant and dynamical Amati relation. Our results indicate that the present quality of GRB data is not good enough to put tight constraints on the cosmological parameters. Hence we perform a joint analysis with the combined data of GRBs and Type Ia Supernovae (SNe) and find that this can considerably enhance cosmological constraints in contrast to solely relying on GRBs.
- Open Access
- 5 February 2022
- Published by Springer Nature in The European Physical Journal C
- Vol. 82 (2) , 1-7
Strong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation
In this paper, we use large scale structure observations to test the redshift dependence of cosmic distance duality relation (CDDR), $$D_\mathrm{L}(1+z)^{-2}/D_\mathrm{A}=\eta (z)$$ , with $$D_\mathrm{L}$$ and $$D_\mathrm{A}$$ , being the luminosity and angular diameter distances, respectively. In order to perform the test, the following data set are considered: strong lensing systems and galaxy cluster measurements (gas mass fractions). No specific cosmological model is adopted, only a flat universe is assumed. By considering two $$\eta (z)$$ parametrizations, It is observed that the CDDR remain redshift independent within $$1.5\sigma $$ which is in full agreement with other recent tests involving cosmological data. It is worth to comment that our results are independent of the baryon budget of galaxy clusters.- 5 February 2022
- Published by Springer Nature in The European Physical Journal C
- Vol. 82 (2) , 1-7
Open AccessStrong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation
In this paper, we use large scale structure observations to test the redshift dependence of cosmic distance duality relation (CDDR), $$D_\mathrm{L}(1+z)^{-2}/D_\mathrm{A}=\eta (z)$$ , with $$D_\mathrm{L}$$ and $$D_\mathrm{A}$$ , being the luminosity and angular diameter distances, respectively. In order to perform the test, the following data set are considered: strong lensing systems and galaxy cluster measurements (gas mass fractions). No specific cosmological model is adopted, only a flat universe is assumed. By considering two $$\eta (z)$$ parametrizations, It is observed that the CDDR remain redshift independent within $$1.5\sigma $$ which is in full agreement with other recent tests involving cosmological data. It is worth to comment that our results are independent of the baryon budget of galaxy clusters. - Open Access
A non-parametric test of variability of Type Ia supernovae luminosity and CDDR
The first observational evidence for cosmic acceleration appeared from Type Ia supernovae (SNe Type Ia) Hubble diagram from two different groups. However, the empirical treatment of SNe Type Ia and their ability to show cosmic acceleration have been the subject of some debate in the literature. In this work we probe the assumption of redshift-independent absolute magnitude $(M_{\mathrm{B}})$ of SNe along with its correlation with spatial curvature ($\Omega_{k0}$) and cosmic distance duality relation (CDDR) parameter ($\eta(z)$). This work is divided into two parts. Firstly, we check the validity of CDDR which relates the luminosity distance ($d_L$) and angular diameter distance ($d_A$) via redshift. We use the Pantheon SNe Ia dataset combined with the $H(z)$ measurements derived from the cosmic chronometers. Further, four different redshift-dependent parametrizations of the distance duality parameter $(\eta(z))$ are used. The CDDR is fairly consistent for almost every parametrization within a $2\sigma$ confidence level in both flat and a non-flat universe. In the second part, we assume the validity of CDDR and emphasize on the variability of $M_{\mathrm{B}}$ and its correlation with $\Omega_{k0}$. We choose four different redshift-dependent parametrizations of $M_{\mathrm{B}}$. The results indicate no evolution of $M_{\mathrm{B}}$ within $2\sigma$ confidence level. For all parametrizations, the best fit value of $\Omega_{k0}$ indicates a flat universe at $2\sigma$ confidence level. However a mild inclination towards a non flat universe is also observed. We have also examined the dependence of the results on the choice of different priors for $H_0$.Open AccessA non-parametric test of variability of Type Ia supernovae luminosity and CDDR
The first observational evidence for cosmic acceleration appeared from Type Ia supernovae (SNe Type Ia) Hubble diagram from two different groups. However, the empirical treatment of SNe Type Ia and their ability to show cosmic acceleration have been the subject of some debate in the literature. In this work we probe the assumption of redshift-independent absolute magnitude $(M_{\mathrm{B}})$ of SNe along with its correlation with spatial curvature ($\Omega_{k0}$) and cosmic distance duality relation (CDDR) parameter ($\eta(z)$). This work is divided into two parts. Firstly, we check the validity of CDDR which relates the luminosity distance ($d_L$) and angular diameter distance ($d_A$) via redshift. We use the Pantheon SNe Ia dataset combined with the $H(z)$ measurements derived from the cosmic chronometers. Further, four different redshift-dependent parametrizations of the distance duality parameter $(\eta(z))$ are used. The CDDR is fairly consistent for almost every parametrization within a $2\sigma$ confidence level in both flat and a non-flat universe. In the second part, we assume the validity of CDDR and emphasize on the variability of $M_{\mathrm{B}}$ and its correlation with $\Omega_{k0}$. We choose four different redshift-dependent parametrizations of $M_{\mathrm{B}}$. The results indicate no evolution of $M_{\mathrm{B}}$ within $2\sigma$ confidence level. For all parametrizations, the best fit value of $\Omega_{k0}$ indicates a flat universe at $2\sigma$ confidence level. However a mild inclination towards a non flat universe is also observed. We have also examined the dependence of the results on the choice of different priors for $H_0$. - Open Access
Strong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation
{In this paper, we use large scale structure observations to test the redshift dependence of cosmic distance duality relation (CDDR), $D_{\rm L}(1+z)^{-2}/D_{\rm A}=\eta(z)$}, with $D_{\rm L}$ and $D_{\rm A}$, being the luminosity and angular diameter distances, respectively. In order to perform the test, the following data set are considered: strong lensing systems and galaxy cluster measurements (gas mass fractions). No specific cosmological model is adopted, only a flat universe is assumed. { By considering two $\eta(z)$ parametrizations, It is observed that the CDDR remain redshift independent within $1.5\sigma$ which is in full agreement with other recent tests involving cosmological data}. It is worth to comment that our results are independent of the baryon budget of galaxy clusters.Open AccessStrong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation
{In this paper, we use large scale structure observations to test the redshift dependence of cosmic distance duality relation (CDDR), $D_{\rm L}(1+z)^{-2}/D_{\rm A}=\eta(z)$}, with $D_{\rm L}$ and $D_{\rm A}$, being the luminosity and angular diameter distances, respectively. In order to perform the test, the following data set are considered: strong lensing systems and galaxy cluster measurements (gas mass fractions). No specific cosmological model is adopted, only a flat universe is assumed. { By considering two $\eta(z)$ parametrizations, It is observed that the CDDR remain redshift independent within $1.5\sigma$ which is in full agreement with other recent tests involving cosmological data}. It is worth to comment that our results are independent of the baryon budget of galaxy clusters.