Weak field and slow motion limits in energy-momentum powered gravity

Abstract

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy-momentum powered gravity (EMPG), viz., the energy-momentum squared gravity (EMSG) of the form $f(T_{\mu \nu }{T}^{\mu \nu })=\alpha (T_{\mu \nu }{T}^{\mu \nu }{)}^{\eta }$ with $\alpha$ and $\eta$ being constants. We have shown that EMPG with $\eta \ge 0$ and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, $M_{\mathrm{ast}}$, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass $M_{\mathrm{eff}}(\alpha ,\eta ,M)=M+M_{\mathrm{empg}}(\alpha ,\eta ,M)$, $M$ being the actual physical mass and $M_{\mathrm{empg}}$ being the modification due to EMPG. Accordingly, while in GR we simply have the relation $M_{\mathrm{ast}}=M$, in EMPG we have $M_{\mathrm{ast}}=M+M_{\mathrm{empg}}$. Within the framework of EMPG, if there is information about the values of $\{\alpha ,\eta \}$ pair or $M$ from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only $M_{\mathrm{ast}}$ alone from astronomical observations, but $M$ and $M_{\mathrm{empg}}$ separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by $|p_{\mathrm{eff}}/{\rho }_{\mathrm{eff}}|\ll 1$ (where $p_{\mathrm{eff}}=p+p_{\mathrm{empg}}$ and ${\rho }_{\mathrm{eff}}=\rho +{\rho }_{\mathrm{empg}}$), whereas this condition leads to $|p/\rho |\ll 1$ in GR.

13 pages, no figures and tables; matches the version published in Physics of the Dark Universe

References in corpus (28)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Confrontation between General Relativity and Experiment
• f(R,T) gravity
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Challenges for $\Lambda$CDM: An update
• f(R,L_m) gravity
• Teleparallel Gravity: From Theory to Cosmology
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations with Lyman-$\alpha$ forests
• Limit to General Relativity in f(R) theories of gravity
• Energy-Momentum Squared Gravity
• Constraints on a Bianchi type I spacetime extension of the standard $\Lambda$CDM model
• Testing spatial curvature and anisotropic expansion on top of the $\Lambda$CDM model
• Temporal Variations in the Sun's Rotational Kinetic Energy
• Screening anisotropy via energy-momentum squared gravity: $\Lambda$CDM model with hidden anisotropy
• Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism
• Low redshift constraints on energy-momentum-powered gravity models
• Jeans analysis in energy-momentum-squared gravity
• Lessons from black hole quasinormal modes in modified gravity
• Emergent Universe from Energy-Momentum Squared Gravity
• Constraining Energy-Momentum-Squared Gravity by binary pulsar observations
• The Mass-Radius relation for Quark Stars in Energy-Momentum Squared Gravity
• Modified gravity and cosmology with nonminimal (derivative) coupling between matter and the Einstein tensor
• Cosmological models in scale-independent energy-momentum squared gravity
• Dynamical analysis of logarithmic energy-momentum squared gravity
• A Survey of Strong Cosmic Censorship Conjecture Beyond Einstein's Gravity
• Observational constraints on nonlinear matter extensions of general relativity: Separable trace power models

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• Constraining the $f$-mode oscillations frequency in Neutron Stars through Universal Relations in the realm of Energy-Momentum Squared Gravity
• Spacetime Curvature as a Probe of Exotic Core Phases in Neutron Stars within Modified Gravity
• Cosmological perturbations in the energy-momentum squared gravity theory: constraints from gravitational wave standard sirens and redshift space distortions