Compare · The Dark Universe

Hu-Sawicki f(R) vs Starobinsky Late-Time f(R)

Geometric Modified Gravity· within family

	Hu-Sawicki f(R) Strongly supported	Starobinsky Late-Time f(R) Strongly supported
Proposed	2007	2007
Key figures	Wayne Hu, Ignacy Sawicki	Alexei Starobinsky
In one sentence	Wayne Hu and Ignacy Sawicki proposed in 2007 a specific functional form of f(R) gravity that drives late-time cosmic acceleration while satisfying solar-system tests via the chameleon mechanism. The construction is one of the most-cited viable f(R) models and has become the canonical reference for modified-gravity searches in cosmological surveys like DES, DESI, Euclid, and LSST.	Alexei Starobinsky proposed in 2007 a separate f(R) construction for late-time cosmic acceleration: Disappearing cosmological constant in f(R) gravity, JETP Lett. 86, 157, a widely cited paper in the field. The framework parameterizes the deviation from Einstein-Hilbert differently from Hu-Sawicki but addresses the same phenomenology: producing late-time acceleration without invoking a true cosmological constant. The two constructions are complementary entries in the geometric-modified-gravity literature.
Predictions	Cosmic acceleration emerges geometrically from the f(R) functional form, without needing a separate cosmological constant Solar-system tests are passed via the chameleon mechanism: the additional scalar degree of freedom is heavy in dense matter and effectively invisible in solar-system observations Structure growth differs from ΛCDM at low redshifts in specific, calculable ways; DES, DESI, Euclid, and LSST should detect or rule out the predicted deviations Specific signatures in galaxy clusters, redshift-space distortions, and weak-lensing cross-correlations distinguish f(R) gravity from a standard dark-energy fluid	Late-time cosmic acceleration emerges from the modified gravitational action without a true cosmological constant; the effective late-time behavior mimics ΛCDM at the background level Structure growth differs from ΛCDM at low redshifts; the deviations are calculable and constrained by weak-lensing and redshift-space-distortion measurements Solar-system tests are passed via a chameleon-like screening mechanism similar to that of Hu-Sawicki Specific differences from Hu-Sawicki in the detailed parameterization can in principle be distinguished by next-generation cosmological surveys, though current data does not favor one over the other strongly
Where it breaks	The chameleon-mechanism construction requires tuning the parameters c_1, c_2, and n to specific ranges; the framework lacks a deep dynamical explanation for these values Current data constrain the f(R) parameter to be very small (\|f_R0\| < 10^-5 or so, meaning the strength of the gravitational modification must be tinier than one part in 100,000), making the deviations from ΛCDM small enough that distinguishing the models requires next-generation surveys The framework does not address the early-universe physics directly; ΛCDM-style inflation is still required separately (cross-reference: Ch.2 Inflation family) Other geometric modified gravity proposals (Starobinsky late-time, sibling variant) cover similar phenomenology with different parameterizations; the choice between them is not yet observationally constrained	Current data does not strongly distinguish Starobinsky late-time f(R) from Hu-Sawicki or from ΛCDM; the choice between these constructions awaits next-generation surveys Like Hu-Sawicki, the framework requires fine-tuning the deviation parameters to specific ranges; the deeper physics origin of these values is not addressed The construction shares the general f(R) limitations: structure growth tensions, σ8 sensitivity, the need for chameleon screening The framework does not directly address the cosmological-constant problem in the sense of explaining why the vacuum energy is small; it relabels the problem rather than solving it
Key unresolved problem	The fine-tuning problem: the chameleon screening that lets f(R) gravity hide inside the solar system forces its departure from ordinary gravity (the parameter \|f_R0\|) to be tiny, and the theory offers no reason why that number is so small.	The look-alike problem: today's data cannot tell Starobinsky's late-time f(R) form apart from the rival Hu-Sawicki form or from plain ΛCDM, because all three predict almost identical skies until next-generation surveys sharpen the picture.
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Hu-Sawicki f(R)

2007 · Strongly supported

Starobinsky Late-Time f(R)

2007 · Strongly supported

Proposed

2007

Key figures

Wayne Hu, Ignacy Sawicki

Alexei Starobinsky

In one sentence

Wayne Hu and Ignacy Sawicki proposed in 2007 a specific functional form of f(R) gravity that drives late-time cosmic acceleration while satisfying solar-system tests via the chameleon mechanism. The construction is one of the most-cited viable f(R) models and has become the canonical reference for modified-gravity searches in cosmological surveys like DES, DESI, Euclid, and LSST.

Alexei Starobinsky proposed in 2007 a separate f(R) construction for late-time cosmic acceleration: *Disappearing cosmological constant in f(R) gravity*, JETP Lett. 86, 157, a widely cited paper in the field. The framework parameterizes the deviation from Einstein-Hilbert differently from Hu-Sawicki but addresses the same phenomenology: producing late-time acceleration without invoking a true cosmological constant. The two constructions are complementary entries in the geometric-modified-gravity literature.

Predictions

Cosmic acceleration emerges geometrically from the f(R) functional form, without needing a separate cosmological constant
Solar-system tests are passed via the chameleon mechanism: the additional scalar degree of freedom is heavy in dense matter and effectively invisible in solar-system observations
Structure growth differs from ΛCDM at low redshifts in specific, calculable ways; DES, DESI, Euclid, and LSST should detect or rule out the predicted deviations
Specific signatures in galaxy clusters, redshift-space distortions, and weak-lensing cross-correlations distinguish f(R) gravity from a standard dark-energy fluid

Late-time cosmic acceleration emerges from the modified gravitational action without a true cosmological constant; the effective late-time behavior mimics ΛCDM at the background level
Structure growth differs from ΛCDM at low redshifts; the deviations are calculable and constrained by weak-lensing and redshift-space-distortion measurements
Solar-system tests are passed via a chameleon-like screening mechanism similar to that of Hu-Sawicki
Specific differences from Hu-Sawicki in the detailed parameterization can in principle be distinguished by next-generation cosmological surveys, though current data does not favor one over the other strongly

Where it breaks

The chameleon-mechanism construction requires tuning the parameters c_1, c_2, and n to specific ranges; the framework lacks a deep dynamical explanation for these values
Current data constrain the f(R) parameter to be very small (|f_R0| < 10^-5 or so, meaning the strength of the gravitational modification must be tinier than one part in 100,000), making the deviations from ΛCDM small enough that distinguishing the models requires next-generation surveys
The framework does not address the early-universe physics directly; ΛCDM-style inflation is still required separately (cross-reference: Ch.2 Inflation family)
Other geometric modified gravity proposals (Starobinsky late-time, sibling variant) cover similar phenomenology with different parameterizations; the choice between them is not yet observationally constrained

Current data does not strongly distinguish Starobinsky late-time f(R) from Hu-Sawicki or from ΛCDM; the choice between these constructions awaits next-generation surveys
Like Hu-Sawicki, the framework requires fine-tuning the deviation parameters to specific ranges; the deeper physics origin of these values is not addressed
The construction shares the general f(R) limitations: structure growth tensions, σ8 sensitivity, the need for chameleon screening
The framework does not directly address the cosmological-constant problem in the sense of explaining why the vacuum energy is small; it relabels the problem rather than solving it

Key unresolved problem

The fine-tuning problem: the chameleon screening that lets f(R) gravity hide inside the solar system forces its departure from ordinary gravity (the parameter |f_R0|) to be tiny, and the theory offers no reason why that number is so small.

The look-alike problem: today's data cannot tell Starobinsky's late-time f(R) form apart from the rival Hu-Sawicki form or from plain ΛCDM, because all three predict almost identical skies until next-generation surveys sharpen the picture.

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