REVIEW
The Cosmological Constant Problems (Talk given at Dark Matter 2000, February, 2000)
Astrophysics · Submitted 12 May 2000 · 3 references
Pith's verdict: A compact, honest 2000 review that states the anthropic case and the quintessence objection cleanly, with a headline probability number that is softer than it reads.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
Weinberg argues that the smallness of the vacuum energy is best explained anthropically, and that quintessence explains nothing.
The reading
What carries the argument
The load-bearing object is the anthropic probability distribution of Eq. (8), $dP(rho_V) = N(rho_V),P_{a priori}(rho_V),d rho_V$, with $N(rho_V)$ supplied by the spherical infall model of galaxy formation: a positive density perturbation inside a sphere, compensated by a negative shell, evolved nonlinearly so that a large enough $rho_V$ suppresses galaxy formation entirely. The upper bound from this model, $rho_V < 500,rho_R,delta_R^3/729$, is what converts a vague statement that the vacuum energy must not be too large into a quantitative distribution. The second piece of machinery is the negative result on tracker quintessence: for $V(varphi) = M^{4+alpha}varphi^{-alpha}$, matching the crossover to the present critical density requires $M^{4+alpha} approx (8pi G)^{-1-alpha/2}H_0^2$, a tuning no less mysterious than the original problem.
Extended reading notes
Core claim
The paper's central claim is that anthropic selection can plausibly solve both cosmological constant problems at once, while quintessence solves neither. The argument runs through a probability distribution $dP(rho_V) = N(rho_V),P_{a priori}(rho_V),d rho_V$, where $N(rho_V)$ is taken as proportional to the fraction of baryons that end up in galaxies. Using the Gunn-Gott spherical infall model as computed by Martel, Shapiro and Weinberg, the integrated distribution in Eq. (10) gives a 5 to 12 percent chance of finding ourselves in a big bang with $Omega_V leq 0.7$, depending on how the density perturbation amplitude is estimated. Because the anthropically allowed range of $rho_V$ is so narrow compared with particle-physics energy densities, the prior $P_{a priori}$ can be treated as flat across it, which is what licenses the calculation. Weinberg also answers the objection of Garriga and Vilenkin that the prior varies appreciably in this range: for potentials of the form $V_1 f(lambda varphi)$ with a simple zero and a very small $lambda$, the fractional variation of the prior across the allowed range is of order $V_{max}/V_1 ll 1$, so flatness is recovered without fine tuning. The closing qualification is that the same flat potentials imply very light bosons, so the anthropic principle can be applied to the cosmological constant but probably not to the masses and charges of elementary particles.
Load-bearing premise
The whole calculation is a conditional probability inside a hypothesized ensemble of big bangs with different vacuum energies, so it says nothing about our universe unless such an ensemble exists and we are typical observers among the members where intelligent life is possible.
Editorial extensions
If this is right
- If the anthropic account holds, the observed vacuum energy needs no cancellation mechanism and no new symmetry; it is a selection effect operating over an ensemble of big bangs.
- The old and new cosmological constant problems become one problem: explaining why the ensemble contains regions with vacuum energies spread across the narrow range in which galaxies can form.
- Tracker quintessence is demoted from a solution to a reformulation, since the crossover condition of Eq. (6) reintroduces a fine tuning of the mass scale $M$ against $H_0$.
- The anthropic route is restricted to the vacuum energy: applying it to particle masses and charges would require a light scalar coupled to ordinary particles, which would already have been seen.
- A measured $Omega_V$ near but somewhat below the median of the predicted distribution is the expected outcome; a value far in the tail would count against the calculation.
Reading between the lines
- The paper's structure suggests a clean observational test: as $Omega_V$ and the primordial perturbation amplitude $sigma$ are pinned down, Eq. (10) becomes a sharp prediction rather than a plausibility argument, and the tail probability for our universe can be read off directly.
- The negative conclusion about quintessence and the positive conclusion about anthropic selection are logically independent, so a future detection of evolving dark energy would not by itself revive a dynamical solution to the old problem.
- The restriction of the anthropic principle to the vacuum energy implies a search strategy: any light scalar invoked to explain other constants of nature must couple to visible particles, so the absence of such particles is itself evidence about which quantities can be selected anthropically.
- The flatness argument for potentials $V_1 f(lambda varphi)$ shifts the explanatory burden onto why the field renormalization constant is large; a natural origin for that large constant would strengthen the case considerably.
Original abstract
The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. | background 1.00 | 0.06 | 0.09 | asserted 1.00 |
| s1 | Several approaches to these problems are reviewed. | contribution 0.74 | 0.36 | 0.03 | asserted 0.77 |
| s2 | Quintessence does not help with either; anthropic considerations offer a possibility of solving both. | result 0.81 | 0.17 | 0.61 | hedged possibility 0.53 |
| s3 | In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else. | interpretation 0.59 | 0.11 | 0.21 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How the literature uses it
172 arXiv papers cite this in 196 sentences
Papers citing it · 111 sentences without a confident label
Uses its data or values 1 paper
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In addition, he noted the huge difference between vacuum energy densities and dark energy density, resulting from the discovery that the density of dark energy is $ε_DE≃[7.17×10^-9]eV^4$ [ref] . ], we are immersed in confusion again.
A Relationship between the Comoving Particle Number and the Effective Cosmological Constant · Introduction · 0.99
Cites it as background 76 papers
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Currently the cosmological constant problem points to understand in a natural way why the vacuum energy density $ρ_v$ is so small; this problem is formulated today to investigate why $ρ_v$ is not only small, but also, comparable to the present mass density of the Universe [ref] .
The Cosmological Constant Problem from the Point of View of String Theory · The Cosmological Constant Problem · 0.89
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The standard picture of a landscape of vacua [ref] , along with an anthropic principle to explain our own universe [ref] , runs into problems not because of any no-go theorem [ref] , or technical hindrances [ref] , but due to obstructions against dS spacetimes ingrained in some fundamental aspects of quantum gravity [ref] .
Four-dimensional de Sitter space is a Glauber-Sudarshan state in string theory · Introduction · 0.84
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These range from anthropic considerations [ref] to k-essence scenarios where dark energy is triggered by matter-radiation equality, coming to dominate within a few billion years [ref] .
Dark energy: EFTs and supergravity · Coincidence problem · 0.87
Discussion
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