A Parameterized Post-Friedmann Framework for Modified Gravity

By Wayne Hu, I. Sawicki. 2007

371 citations recorded by the source corpus.

We develop a parametrized post-Friedmann (PPF) framework which describes three regimes of modified gravity models that accelerate the expansion without dark energy. On large scales, the evolution of scalar metric and density perturbations must be compatible with the expansion history defined by distance measures. On intermediate scales in the linear regime, they form a scalar-tensor theory with a modified Poisson equation. On small scales in dark matter halos such as our own galaxy, modifications must be suppressed in order to satisfy stringent local tests of general relativity. We describe these regimes with three free functions and two parameters: the relationship between the two metric fluctuations, the large and intermediate scale relationships to density fluctuations, and the two scales of the transitions between the regimes. We also clarify the formal equivalence of modified gravity and generalized dark energy. The PPF description of linear fluctuation in f(R) modified action and the Dvali-Gabadadze-Porrati braneworld models show excellent agreement with explicit calculations. Lacking cosmological simulations of these models, our nonlinear halo-model description remains an ansatz but one that enables well-motivated consistency tests of general relativity. The required suppression of modifications within dark matter halos suggests that the linear and weakly nonlinear regimes are better suited for making a complementary test of general relativity than the deeply nonlinear regime.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/585390c7ac6cb7b7cd6bf2d18181c0706726d3b4

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Citations in the corpus

Probing the theory of gravity with gravitational lensing of gravitational waves and galaxy surveys (2019, background): “(9) (Carroll et al. 2006; Bean et al. 2007; Hu & Sawicki 2007; Schmidt 2008; Silvestri et al. 2013; Baker et al. 2015; Lombriser & Taylor 2016; Lombriser & Lima 2017; Saltas et al. 2014; Baker & Bull 2015; Slosar et al. 2019) such as (i) g(k, z) 6= 0, (ii) the modified Poisson Equation, (iii)…”
DESI 2024: reconstructing dark energy using crossing statistics with DESI DR1 BAO data (2024, methodology): “To allow for a phantom equation of state, w ( z ) − 1, we rely on the Parametrized-Post Friedmann (PPF) framework [60], as implemented in class .”
Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods (2019, methodology): “Here, as well as in all models including non-Λ dark energy, we use the PPF prescription [67] for incorporating dark energy perturbations.”
LATE-TIME COSMOLOGY WITH 21 cm INTENSITY MAPPING EXPERIMENTS (2014, background): “There is great variety in the effects that different modifications to gravity have on the linear growth history; the space of theories is complex and has proved difficult to parameterize in a simple way (Hu & Sawicki 2007; Battye & Pearson 2012; Baker et al. 2013).”
Cosmological Parameters from Observations of Galaxy Clusters (2011, background): “These include frameworks that consistently parametrize departures from General Relativity (GR; Hu & Sawicki 2007; Amin, Wagoner & Blandford 2008; Daniel et al. 2010); full, alternative theories such as the Dvali-Gabadadze-Porrati (DGP) braneworld gravity (Dvali, Gabadadze & Porrati 2000); f(R)…”
Gauge fields and inflation (2012, background): “A non-zero a(2)πS is a feature present in the inflationary/cosmological models with modified gravity [136] and causes difference between the two Bardeen potentials Φ and Ψ, this provides a way to trace its observable effects by affecting the structure formation analysis, for a more detailed discussi”
FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2008, neutral): “…et al. 2006; Doré et al. 2007; Linder & Cahn 2007; Upadhye 2007; Zhang et al. 2007; Yamamoto et al. 2007; Chiba & Takahashi 2007; Bean et al. 2007; Hu & Sawicki 2007; Song et al. 2007; Daniel et al. 2008; Jain & Zhang 2007; Bertschinger & Zukin 2008; Amin et al. 2007; Hu 2008), as well as for…”
Modified Gravity and Cosmology (2011, methodology): “[482] perform a thorough test of the self-accelerating model using the PPF approach of [627, 630].”
SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2010, neutral): “…et al. 2006; Doré et al. 2007; Linder & Cahn 2007; Upadhye 2007; Zhang et al. 2007; Yamamoto et al. 2007; Chiba & Takahashi 2007; Bean et al. 2007; Hu & Sawicki 2007; Song et al. 2007; Starobinsky 2007; Daniel et al. 2008; Jain & Zhang 2008; Bertschinger & Zukin 2008; Amin et al. 2008; Hu 2008)…”