Cosmological implications of scale-independent energy-momentum squared
  gravity: Pseudo nonminimal interactions in dark matter and relativistic
  relics
  In this paper, we introduce a scale-independent energy-momentum squared
gravity (EMSG) that allows different gravitational couplings for different
types of sources, which may lead to scenarios with many interesting
applications/implications in cosmology. In the present study, to begin with, we
study a modification of the $\Lambda$ cold dark matter ($\Lambda$CDM) model,
where photons and baryons couple to the spacetime as in general relativity,
while the cold dark matter and relativistic relics (neutrinos and any other
relativistic relics) couple to the spacetime in accordance with EMSG. This
scenario induces pseudo nonminimal interactions on these components, leading to
modification at both the background and perturbative levels. A consequence of
this scenario is that the dimensionless free parameter of the theory may induce
direct changes on the effective number of the relativistic species, without the
need to introduce new extra species. In order to quantify the observational
consequences of the cosmological scenario, we use the cosmic microwave
background Planck data (temperature, polarization, and lensing power spectrum)
and baryonic acoustic oscillations data. We find that the free model parameter
is too small to induce statistically significant corrections on the
$\Lambda$CDM model due to EMSG. We deduce that the model presented here is
quite rich with promising cosmological applications/implications that deserve
further investigations.
