Linear Nash-Greene fluctuations on the evolution of $S_8$ and $H_0$ tensions

Understand

We present the perturbation equations in an embedded four space-time from the linear Nash-Greene fluctuations of background metric.

• In the context of a five-dimensional bulk, we show that the cosmological perturbations are only propagated by the gravitational tensorial field equation.
• In Newtonian conformal gauge, we study the matter density evolution in sub-horizon regime and on how such scale may be affected by the extrinsic curvature.
• We apply a joint likelihood analysis to the data by means of the Markov Chain Monte Carlo (MCMC) method for parameter estimation using a pack of recent datasets as the Pantheon Supernovae type Ia, the Baryon Acoustic Oscillations (BAO) from DR12 galaxy sample and Dark Energy Survey (DESY$1$).