Large scale structure constraints and matter power spectrum in $f (Q,\mathcal{L}_{m})$ gravity

TL;DR

This work investigates large-scale structure growth and the matter power spectrum in f(Q, L_m) gravity by combining dynamical-system methods for two explicit models with a 1+3 covariant perturbation formalism. It derives autonomous background equations for Model A and Model B, then obtains perturbation equations that yield the evolution of the matter density contrast and nonmetricity fluctuations, subsequently computing matter power spectra. Using MCMC with diverse observational data, the study finds Model A can be compatible with data sets while Model B cannot, highlighting how nonmetricity-matter couplings influence growth and cosmological tensions. The results demonstrate that f(Q, L_m) gravity can mimic ΛCDM at the background level but leaves distinguishable signatures in structure growth and the matter power spectrum, offering a viable path to address H0 and σ8 tensions with future, more comprehensive data analyses.

Abstract

In the present work, we take into account the dynamical system analysis to investigate the matter power spectrum within the framework of the $f(Q,\mathcal{L}_{m})$ gravitational theory. After obtaining autonomous dynamical system variables for two different particular pedagogical choices of $f(Q,\mathcal{L}_{m})$ models (A and B), we derive the full system of perturbation equations using the $1+3$ covariant formalism to study the matter fluctuations. We present and solve the energy density perturbation equations to obtain the energy density contrast, which decays with redshift for both models for a particular choice of model parameters. After obtaining the numerical results of the density contrast, we computed the matter spectra for each model and conducted a comparative analysis with the $Λ$CDM. Furthermore, by employing the Markov Chain Monte Carlo (MCMC) analysis,the model parameters were constrained using a combination of different observational data sets to improve the robustness and accuracy of the parameter estimation. Our results indicate that only model A can be compatible with the considered observational data sets.

Figures (12)

• Figure 1: Plot of energy density contrast ($\delta$) versus redshift ($z$) for different values of constant parameters of Eq. (\ref{['eq3.12']}) and eq. (\ref{['eq3.13']}) of model A in the context of $f(Q, \mathcal{L}_{m}$ gravity. The choice of values of model parameters was done basing on the constrained parameters obtained in the work done in hazarika2024f
• Figure 2: Plot of energy density contrast ($\delta$) versus redshift $z$ for different values of constant parameters of Eq. (\ref{['eq3.12']}) and eq. (\ref{['eq3.13']}) of model A. The choice of values of model parameters was done basing on the constrained parameters obtained in the work done in hazarika2024f for model B
• Figure 3: Plot of energy density contrast ($\delta$) versus redshift $z$ for different values of constant parameters of eq. (\ref{['eq3.14']}) and eq. (\ref{['eq3.15']}) of model B in the context of $f(Q, \mathcal{L}_{m})$ gravity.
• Figure 4: Plot of energy density contrast $\delta$ versus redshift $z$ for different values of constant parameters of eq. (\ref{['eq3.14']}) and eq. (\ref{['eq3.15']}) of model B in the context of $f(Q, \mathcal{L}_{m})$ gravity.
• Figure 5: Plot matter power spectra for different values of $\gamma$ for $\alpha=0.3$ and $\beta=-0.0001$ of eq. (\ref{['eq4.1']}) and eq. (\ref{['eq4.2']}) of model A in the context of $f(Q, \mathcal{L}_{m})$ gravity. We use the initial conditions $\Delta(z)=10^{-5}$, $\Delta'(z)=0$, $\mathcal{C}(z)=10^{-5}$, $\mathcal{C}'(z)=0$.