Mohammad Malekjani

In this work, we impose observational constraints on the thermodynamics-gravity conjecture, based on the modified Tsallis entropy, known as Tsallis cosmology, within the context of the Cosmographic approach. We utilize the latest observational datasets from DESI BAO 2024 and the PantheonPlus sample of SNIa. For comparison, we conduct our analysis using the standard flat- $$\varLambda $$ Λ CDM cosmology as the concordance model. Our cosmographic analysis reveals that both models exhibit good consistency with observations when utilizing the DESI BAO dataset and the PantheonPlus SNIa sample. Additionally, the combination of DESI BAO and PantheonPlus observations demonstrates full consistency between the models and the Cosmographic approach, provided there is no external prior on the sound horizon of baryons at the drag epoch, $$r_d$$ r d . When incorporating the Planck prior on $$r_d$$ r d , our analysis supports notable deviations of the Tsallis and $$\varLambda $$ Λ CDM models from the confidence bands of the Cosmographic approach. These deviations can be directly related to this physical fact that cosmological models like Tsallis and $$\varLambda $$ Λ CDM can not fit the low-redshift SNIa data calibrated by Cepheid observations and DESI BAO observations with an external high-redshift CMB prior on $$r_d$$ r d , simultaneously.

In the context of the gravity-thermodynamics conjecture based on the Tsallis entropy-area relation, we investigate the standard $$\varLambda $$ Λ CDM cosmology and examine some potential deviations from it. Utilizing recent updates from geometrical datasets, including the DESI BAO measurements (2024), Planck CMB anisotropy measurements (2018), and the Pantheon+ catalogue for SNIa (2022), we conduct a thorough analysis via the window of Tsallis cosmology. In the first step, our analysis reveals no significant deviation from the standard model when using DESI BAO data alone, Pantheon+ data alone, or a combination of both. In the next step, we incorporate all datasets by adding the CMB data to our analysis, indicating a potential deviation from the standard model within the framework of Tsallis cosmology. Imposing the Planck prior to the sound horizon at the baryon drag epoch, we observe support for the standard model and consistency between our constraints on the Hubble constant and the Planck value. Finally, we compare the Tsallis and $$\varLambda $$ Λ CDM cosmologies using the Akaike Information Criterion (AIC).

In this study, we present an analysis of the standard flat-$\Lambda$CDM (Lambda cold dark matter) model using a cosmographic approach, incorporating recent Dark Energy Survey Instrument (DESI) baryon acoustic oscillation (BAO) observations and Type Ia Supernova (SNIa) catalogues, including Dark Energy Survey Supernova 5 Year Release (DES-SN5YR) and Pantheon + compilations. We find full consistency between the standard model and the cosmographic approach when considering DESI BAO and SNIa catalogues independently. When combining DESI BAO with SNIa data, we examine the impact of the Planck prior on the sound horizon at the drag epoch, $r_d$, and the Cepheid prior on the absolute magnitude, M. Applying the Planck prior on $r_d$ alone yields an $H_0$ value consistent with the Planck measurement, while applying the Cepheid prior on M alone results in an $H_0$ value consistent with the SH0ES measurement. Without any priors, the $H_0$ value obtained has a large error margin, reconciling the Planck and SH0ES measurements. In all cases where individual priors are applied, we observe no significant tension between the flat-$\Lambda$CDM model and the cosmographic approach. However, when both Planck and Cepheid priors are applied simultaneously, significant tensions arise between the model and cosmography. This tension is even more pronounced when excluding LRG1 and LRG2 from the DESI measurements. These results indicate that the standard model cannot simultaneously reconcile high-redshift Planck cosmic microwave background observations and local Cepheid measurements. This discrepancy supports the possibility of new physics beyond the standard model or, alternatively, the presence of unrecognized systematic errors in the observational data.

Despite the broad successes of the flat $Λ$CDM model and its fitness to the various cosmological observations, it confronts challenges stemming from anomalies in the measurements of the Hubble constant ($H_0$) and the amplitude of matter fluctuations ($σ_8$). These inconsistencies have necessitated a reassessment of the model parameters, with a particular focus on their potential dependence on redshift. This study pioneers a new investigation to probe this redshift dependency by generating mock data simulated from observational data of Type Ia supernovae (SNIa) and cosmic chronometers (CC), thereby increasing the data density in this field. By sorting the data into high-redshift and low-redshift bins, we aim to refine the cosmological constraints on the parameters of the $Λ$CDM model and determine whether the noted dependence on redshift is due to a lack of high-redshift observational data or if they signify intrinsic issues within the model itself. Our approach employs the Markov Chain Monte Carlo (MCMC) algorithm to minimize the $χ^2$ function, thus tightening the cosmological constraints. Our findings within the mock analysis reveal discrepancies between the values of $Ω_{m0}$ and $H_0$ derived from the mock data bins with high redshift and low redshift, indicating the potential deviation of the standard $Λ$ CDM cosmology from the high-redshift SNIa and CC data. If this deviation proposes a new physics beyond the standard model, then with better quality future data tracking the new physics, these discrepancies will be statistically significant.

Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first put constraints on the cosmographic parameters in the context of the various model-independent cosmographic methods reconstructed from the Taylor 4th and 5th order expansions and the Padé (2,2) and (3,2) polynomials of the Hubble parameter, respectively. We then reconstruct the distance modulus in the framework of cosmographic methods and calculate the percentage difference between the distance modulus of the cosmographic methods and that of the standard model. The percentage difference is minimized when the Padé approximation is used which means that the Padé cosmographic method is sufficiently suitable for reconstructing the distance modulus even at high-redshifts. In the next step, using the real observational data for the Hubble diagrams of SNIa, QSOs, gamma-ray-bursts (GRBs), and observations from baryon acoustic oscillations (BAO) in two sets of the low-redshift combination ($\mathrm{SNIa}+\mathrm{QSOs}+\mathrm{GRBs}+\mathrm{BAO}$) embracing the redshift range of $0.01<z<2.26$ and the high-redshift combination ($\mathrm{SNIa}+\mathrm{QSOs}+\mathrm{GRBs}$) which covers a redshift range of $0.01<z<5.5$, we put observational constraints on the cosmographic parameters of the Padé cosmography and also the standard model. Our analysis indicates that Padé cosmographic approaches do not reveal any cosmographic tension between the standard model and the observational data. We also confirm this result, using the statistical AIC criteria. Finally, we put the cosmographic method in the redshift-bin data and find a larger value of ${\mathrm{\Omega }}_{m0}$ extracted from $s_0$ parameter compared with those of the $q_0$ parameter and Planck-$\mathrm{\Lambda }\mathrm{CDM}$ values.

Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first put constraints on the cosmographic parameters in the context of the various model-independent cosmographic methods reconstructed from the Taylor $4^{th}$ and $5^{th}$ order expansions and the Pade (2,2) and (3,2) polynomials of the Hubble parameter, respectively. We then reconstruct the distance modulus in the framework of cosmographic methods and calculate the percentage difference between the distance modulus of the cosmographic methods and that of the standard model. The percentage difference is minimized when the Pade approximation is used which means that the Pade cosmographic method is sufficiently suitable for reconstructing the distance modulus even at high-redshifts. In the next step, using the real observational data for the Hubble diagrams of SNIa, QSOs, gamma-ray-bursts (GRBs), and observations from baryon acoustic oscillations (BAO) in two sets of the low-redshift combination (SNIa+QSOs+GRBs+BAO) embracing the redshift range of $0.01<z<2.26$ and the high-redshift combination (SNIa+QSOs+GRBs) which covers a redshift range of $0.01< z < 5.5$, we put observational constraints on the cosmographic parameters of the Pade cosmography and also the standard model. Our analysis indicates that Pade cosmographic approaches do not reveal any cosmographic tension between the standard model and the observational data. We also confirm this result, using the statistical AIC criteria. Finally, we put the cosmographic method in the redshift-bin data and find a larger value of $\Omega_{m0}$ extracted from $s_0$ parameter compared with those of the $q_0$ parameter and Planck-$\Lambda$CDM values.

In this paper, we study the power-law $f(T)$ model using Hubble diagrams of type Ia supernovae (SNIa), quasars (QSOs), Gamma Ray Bursts (GRBs) and the measurements from baryonic acoustic oscillations (BAO) in the framework of the cosmographic method. Using mock data for SNIa, QSOs and GRBs generated based on the power-law $f(T)$ model, we show whether different cosmographic methods are suitable to reconstruct the distance modulus or not. In particular, we investigate the rational PADE polynomials $(3,2)$ and $(2,2)$ in addition to the fourth- and fifth- order Taylor series. We show that PADE $(3,2)$ is the best approximation that can be used in the cosmographic method to reconstruct the distance modulus at both low and high redshifts. In the context of PADE $(3,2)$ cosmographic method, we show that the power-law $f(T)$ model is well consistent with the real observational data from the Hubble diagrams of SNIa, QSOs and GRBs. Moreover, we find that the combination of the Hubble diagram of SNIa and the BAO observation leads to better consistency between the model-independent cosmographic method and the power-law $f(T)$ model. Finally, our observational constraints on the parameter of the effective equation of state of DE, described by the power-law $f(T)$ model, show the phantom-like behavior, especially when the BAO observations are included in our analysis.