Jerk, snap, and the cosmological equation of state

By Matt Visser. 2003

581 citations recorded by the source corpus.

Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be 'predictive', in the sense that once some a priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a 'retrodictive' approach might usefully take observational data concerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk and snap—the second, third and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak, and are likely to remain weak for the foreseeable future.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/0e6713292dff65170484fc2fa68f801b2293af68

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In Astronomy and Astrophysics

1. A. Riess
2. A. Filippenko
3. S. Jha
4. Thanu Padmanabhan
5. W. Freedman
6. S. Vagnozzi
7. Yi Wang
8. Weidong Li

Citations in the corpus

• Cosmological parameters from supernova observations: A critical comparison of three data sets (2003, background): “…2002; Maor et al. 2002; Weller & Albrecht 2002; Gerke & Efstathiou 2002; Rowan-Robinson 2002; Linder & Jenkins 2003; Padmanabhan & Choudhury 2003; Visser 2004; Caresia, Matarrese, & Moscardini 2004; Alcaniz 2004; Wang & Mukherjee 2004; Novello, Perez Bergliaffa, & Salim 2003; Knop et al.…”
• Evidence for anisotropy of cosmic acceleration (2018, methodology): “…assumptions about the matter content or the dynamics, we use the kinematic Taylor series expansion of the luminosity distance up to the third term (Visser 2004) as follows: dL(zhel) = czhel H0 { 1+ 1 2 [1−q0]zhel− 1 6 [1−q0−3q20+ j0+ kc2 H20a 2 0 ]z2hel } , (5) where q ≡ −äa/ȧ2 is the cosmic…”
• Holographic dark energy (2016, methodology): “erent letters of the alphabet have been used to describe higher derivatives of a(t). For examples, A 3 corresponds to the jerk j, A 4 corresponds to the snap s, and A 5 corresponds to the lerk l(See [234, 235, 236] and references therein). These quantities are called geometrical diagnostic in the se”
• The Local Perspective on the Hubble Tension: Local Structure Does Not Impact Measurement of the Hubble Constant (2019, methodology): “According to Visser (2004), using the FLRW metric, the Taylor expansion of luminosity distance as a function of redshift about z=0 is D z H q j cz H q z q q j z O z ; , , 1 1 2 1 3 6 , 3 L k FLRW 0 0 0 0 0 0 0 2 0 2 3 = + - - - - + -”
• Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities and extremality events (2005, background): “The central question in cosmology is now the prediction, or rather retro-diction, of the history of the scale factor a(t) [ 5 , 6]. The key dynamical equations (assuming applicability of the Einstein equations of general relativity to cosmology in the large, an assumption which at least some cosmolo”
• A REDETERMINATION OF THE HUBBLE CONSTANT WITH THE HUBBLE SPACE TELESCOPE FROM A DIFFERENTIAL DISTANCE LADDER (2009, methodology): “We may relate the observables of SN Ia distance and redshift, z, to the scale factor of the Universe, a, by expanding a(t) using the definitions H(t) = +ȧ/a, q(t) = −(ä/a)(ȧ/a)−2, j(t) = +( ˙̈a/a)(ȧ/a)−3 (10) (cf. Visser 2004).”
• MODEL-INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION FROM BARYON ACOUSTIC OSCILLATIONS (2014, background): “One such diagnostic is the Statefinder r = ...a /aH 3 (also called the jerk) whose value remains at unity only in ΛCDM (Sahni et al. 2003; Alam et al. 2003) (also see Chiba & Nakamura 1998; Visser 2004).”
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team (2021, methodology): “…history and for z> 0 as = + - - - - + + -{ }[ ] [ ] ( ) ( )a cz q z q q j z O z mlog 1 12 1 16 1 3 0.2 , 4B B0 0 02 0 2 3 0 measured from a set of SNe Ia (z m, B 0), where z is the redshift due to expansion, q0 is the deceleration parameter, and j0 is the jerk (see Visser 2004 for definitions).”
• RECONSTRUCTING DARK ENERGY (2006, unknown): “Visser,2004,Class.”
• The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch (2019, methodology): “As in Freedman et al. (2009), we use a simple Taylor series expansion to derive the luminosity distance and the distance modulus as a function of redshift (Caldwell & Kamionkowski 2004; Visser 2004).”
• Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes (2007, background): “the cosmological fluid violates the strong energy condition [SEC], and provides tantalizing hints that the NEC might possibly be violated in a classical regime [32, 33, 34].”