Beltran Jimenez, J., Heisenberg, L., Olmo, G. J., & Rubiera-Garcia, D. (2018). Born-Infeld inspired modifications of gravity. Phys. Rep., 727, 1–129.
Abstract: General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.
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Reichardt, C. L., de Putter, R., Zahn, O., & Hou, Z. (2012). New limits on early dark energy from the South Pole telescope. Astrophys. J. Lett., 749(1), L9–5pp.
Abstract: We present new limits on early dark energy (EDE) from the cosmic microwave background (CMB) using data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite on large angular scales and South Pole Telescope on small angular scales. We find a strong upper limit on the EDE density of Omega(e) < 0.018 at 95% confidence, a factor of three improvement over WMAP data alone. We show that adding lower-redshift probes of the expansion rate to the CMB data improves constraints on the dark energy equation of state, but not the EDE density. We also explain how small-scale CMB temperature anisotropy constrains EDE.
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