Luminosity-Temperature Relation as a Probe for Modified Gravity

Abstract

We investigate the luminosity-temperature ($L$-$T$) relation of galaxy clusters as a probe for testing modified gravity (MG) theories, focusing on $f(R)$ gravity and symmetron models. Using an improved semi-analytic framework that incorporates angular momentum acquisition, dynamical friction, and shock heating within the modified punctuated equilibrium model, we compare predictions against hydrodynamical simulations and observational data. While massive clusters remain largely screened and follow standard $Λ$CDM predictions, low-mass systems ($kT \lesssim 1-2$ keV) exhibit systematic deviations characterized by steeper $L$-$T$ slopes in MG scenarios. Crucially, we demonstrate that these signatures cannot be mimicked by conventional astrophysical processes such as feedback or angular momentum effects, which primarily affect normalization rather than curvature. Our results establish the $L$-$T$ relation as a robust diagnostic tool for distinguishing general relativity from screened MG theories, with the strongest discriminatory power emerging at group scales accessible to current and future X-ray surveys. Moreover, a normalized reduced $χ^2$ analysis of the $L$-$T$ relation shows that MG models provide significantly better agreement with observational data than $Λ$CDM, with several realizations achieving excellent fits while the $Λ$CDM model consistently performs worst.

Figures (4)

• Figure 1: The luminosity-temperature ($L$-$T$) relation for the $f(R)$ gravity models compared with the standard $\Lambda$CDM scenario. The black curve represents the $\Lambda$CDM prediction, while the stacked galaxy clusters are shown by red and blue circles, blue squares, and black stars. Also the corresponding data from XXL survey is presented as cyan points 2016AA...592A...3G. The cyan shaded region denotes the 68% confidence interval obtained from the continuous formation model [Eq. \ref{['eq:LT_final']}] and the reference model of 2002ApJ...564..669A. The red, blue, and green curves correspond to the $f(R)$ models with three different parameters $f_{R0}=10^{-4}$, $10^{-5}$, and $10^{-6}$, respectively.
• Figure 2: Similar to Fig. \ref{['fig1']}, but for symmetron model. The black curve denotes the $\Lambda$CDM prediction, whereas the red, pink, brown, and yellow curves correspond to the symmetron models SymA, SymB, SymC, and SymD, respectively.
• Figure 3: Normalized $\tilde{\chi}^2$ analysis for the $f(R)$ gravity models, while comparing with the corresponding result from $\Lambda$CDM model.
• Figure 4: Similar to Fig. \ref{['fig3']}, but for symmetron models.