Physical Review D, ( ISI ), Volume (94), No (4), Year (2016-8) , Pages (1-10)

Title : ( Energy-momentum squared gravity )

Authors: Mahmood Roshan , Fatimah Shojai ,

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A new covariant generalization of Einstein’s general relativity is developed which allows the existence of a term proportional to TαβTαβ in the action functional of the theory (Tαβ is the energy-momentum tensor). Consequently, the relevant field equations are different from general relativity only in the presence of matter sources. In the case of a charged black hole, we find exact solutions for the field equations. Applying this theory to a homogeneous and isotropic spacetime, we find that there is a maximum energy density ρmax, and correspondingly a minimum length amin, at the early Universe. This means that there is a bounce at early times, and this theory avoids the existence of an early-time singularity. Moreover, we show that this theory possesses a true sequence of cosmological eras. We also argue that, although in the context of the standard cosmological model the cosmological constant Λ does not play any important role in the early times and becomes important only after the matter-dominated era, in this theory the “repulsive” nature of the cosmological constant plays a crucial role at early times in resolving the singularity.


, energy-momentum squared gravity, modified gravity, cosmology, dynamical systems
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author = {Roshan, Mahmood and Fatimah Shojai},
title = {Energy-momentum squared gravity},
journal = {Physical Review D},
year = {2016},
volume = {94},
number = {4},
month = {August},
issn = {2470-0010},
pages = {1--10},
numpages = {9},
keywords = {energy-momentum squared gravity; modified gravity; cosmology; dynamical systems},


%0 Journal Article
%T Energy-momentum squared gravity
%A Roshan, Mahmood
%A Fatimah Shojai
%J Physical Review D
%@ 2470-0010
%D 2016