Screening $$\Lambda $$ in a new modified gravity model

Abstract

Abstract We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term $$f(T_{\mu \nu }T^{\mu \nu })=\alpha \ln (\lambda \,T_{\mu \nu }T^{\mu \nu })$$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>T</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>α</mml:mi><mml:mo>ln</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>λ</mml:mi><mml:mspace/><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>T</mml:mi><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, envisaged as a correction, to the Einstein–Hilbert action with cosmological constant $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>. The choice of this modification is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmologies, in particular, an extension of the standard $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>CDM model. EMLG provides an effective dynamical dark energy passing below zero at large redshifts, accommodating a mechanism for screening $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> in this region, in line with suggestions for alleviating some of the tensions that arise between observational data sets within the standard $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>CDM model. We present a detailed theoretical investigation of the model and then constrain the free parameter $$\alpha '$$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>α</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>, a normalisation of $$\alpha $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>, using the latest observational data. The data does not rule out the $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>CDM limit of our model ($$\alpha '= 0$$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>α</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>), but prefers slightly negative values of the EMLG model parameter ($$\alpha '= -0.032\pm 0.043$$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>α</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>0.032</mml:mn><mml:mo>±</mml:mo><mml:mn>0.043</mml:mn></mml:mrow></mml:math>), which leads to the screening of $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>. We also discuss how EMLG relaxes the persistent tension that appears in the measurements of $$H_0$$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> within the standard $$\Lambda $$<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>CDM model.