DESI and fast radio burst used to constrain modified theories of gravity

TL;DR

This work evaluates a non-commutative Starobinsky-type $f(R)$ gravity in a flat FLRW universe, deriving a modified Friedmann framework characterized by a dimensionless form $\beta^2 E(z)^2 = \Omega_{0m}[(1+z)^3-1] + \frac{3\Omega_{0r}}{4}[(1+z)^4-1] + \beta^2$ and a near-constant $\tilde{R}$ around $\sim 3$. An MCMC analysis integrating cosmic chronometers, SNIa, HIIG, QSO, DESI-DR1 BAO, and FRBs tests the model against data, constraining $\Theta=\{h,\Omega_{0b},\Omega_{0m},\beta\}$ and quantifying correlations with observables like the deceleration transition redshift $z_T$ and $q_0$. The results show that, while the model can fit late-time data without BAO, the inclusion of BAO data yields strong disfavour relative to $\Lambda$CDM, with FRBs notably shifting some posteriors (e.g., $\Omega_{0b}$) and tightening or shifting $\nu$ and $\beta$ correlations. Overall, DESI and FRBs provide valuable constraints on this modified gravity scenario, though BAO data highlight tensions that warrant further investigation into non-commutative cosmology and high-redshift behavior.

Abstract

This paper is devoted to the study of the viability of DESI and the fast radio burst to constrain the free parameters of modified theories of gravity. Thus, we present a model supported in $f(R)$ gravity involving a function of the Ricci scalar named Starobinsky-type with the peculiarity that the non-commutative essence is intrinsic to the coefficients. Additionally, to understand the dynamics within a flat Friedmann-Lemaitre-Robertson-Walker universe, we explore the possibility of deriving a Friedman equation (in measure) that results from an adequate mathematical treatment. As we mentioned previously, to test the outlined model, a Monte Carlo Markov chain analysis is implemented, using cosmic chronometers, type Ia supernovae, Hydrogen II galaxies, Intermediate-luminosity quasars, Baryon Acoustic oscillations and Fast Radio Bursts data, to constraint the free parameters of the model and presenting $H(z)$, $q(z)$ and $ω_{eff}(z)$. The final results are compared with the $Λ$CDM model and a robust discussion is presented about the viability of DESI and fast radio burst to constraint free parameters in specific to a modified theory of gravity.

Figures (3)

• Figure 1: 1D posterior distributions and 2D contours at $1\sigma$ (inner region) and $3\sigma$ (outermost region) CL for $f_{nc}(R)$ model.
• Figure 2: Reconstruction of the Hubble parameter (left column), the deceleration parameter (middle column) and the effective EoS of the Universe for the $f_{nc}(R)$ cosmology in the redshift range $-1<z<2.2$ using different data combinations. The standard $\Lambda$CDM model is included as red dashed lines.
• Figure 3: 1D posterior distributions and 2D contours at $1\sigma$ (inner region) and $3\sigma$ (outermost region) CL for $f_{nc}(R)$ model considering Uniform priors on $0.2<h<1$ and $0.1<\Omega_{0m}<1$.

Theorems & Definitions (2)

• Lemma B.1
• Proof B.1