Minimally modified gravity fitting Planck data better than $$\Lambda $$ CDM
Katsuki Aoki, Antonio De Felice, Shinji Mukohyama, Karim Noui, Michele Oliosi, Masroor C. Pookkillath
Abstract
Abstract We study the phenomenology of a class of minimally modified gravity theories called $$f(\mathcal {H})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a 3-parameter family of the function f . Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of $$f(\mathcal {H})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theories fits the data significantly better than the standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model, in particular by modifying gravity at intermediate redshifts, $$z\simeq 743$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>743</mml:mn> </mml:mrow> </mml:math> .