D物质宇宙中的引力波传播与引力子质量效应

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"D物质宇宙中重力的传播" 在物理学领域，这篇由Thomas Elghozi、Nick E. Mavromatos和Mairi Sakellariadou共同撰写的开放获取文章探讨了引力波在D物质宇宙中的传播特性。文章发表在《欧洲物理杂志C》（Eur.Phys.J.C）2017年第77卷，编号445，DOI为10.1140/epjc/s10052-017-4998-z。这篇理论物理和宇宙学的研究文章深入研究了引力子在D物质环境中的行为。引力波的检测，特别是在激光干涉引力波天文台（aLIGO）对合并黑洞的探测中取得的突破，激发了作者对引力波在D物质宇宙中传播的研究兴趣。D物质是一种假设的物质形式，它与大规模结构的形成和通货膨胀理论相兼容。在D物质宇宙中，由于D粒子的Born-Infeld动力学，产生了反冲速度场的凝聚体，这使得引力子获得了有效质量。这个现象暗示着引力子与D粒子之间存在相互作用。文章指出，D粒子的引力能量作为暗物质的一个组成部分，其折射率超过了光速，从而导致了与引力子的竞争性效应。作者们分析了凝聚条件，特别是当反冲速度的量子波动相对较大时，可能在当前的宇宙阶段，引力子的感应质量和凝聚水的影响可能会比反冲速度的大小大几个数量级，甚至可能与现今的宇宙学常数有关。为了限制引力子的质量，作者利用了aLIGO的数据和脉冲星定时观测提供的最严格的边界。在具有腔内引力子的场景下，高能宇宙物质也会受到重力切伦科夫效应的影响，这在观察到的超高能宇宙射线中得到了进一步限制。如果假设这些宇宙射线源自银河系外，基于重力契伦科夫效应的量子凝聚强度的界限与aLIGO的测量界限相同，这与假定宇宙射线起源于银河系内的情况相比，相应界限会显得更弱。这项工作提供了对引力子性质和D物质宇宙模型的新见解，同时也为未来的引力波探测和宇宙学研究提供了理论基础。通过研究引力子在D物质环境中的传播，科学家们可以更好地理解宇宙的暗物质成分以及引力的传播机制，这对于构建更精确的宇宙模型至关重要。

Eur. Phys. J. C (2017) 77 :445 Page 3 of 15 445

where α = α



, F = d ∧ A is the ﬁeld strength of the

vector ﬁeld and −

G

μν

 is a dilaton-independent term

of ﬂux ﬁelds, assumed condensed (...), which is induced

by the bulk geometry and serves the purpose of keeping any

cosmological-constant terms on the brane universe in the cur-

rent era (we are interested in here) positive and small, in

accordance to observations [29]. We shall deﬁne the various

other quantities appearing in Eq. (2.1) below.

An important point we would like to stress is that the action

(2.1) is derived by string world-sheet conformal invariance

considerations in the framework of Lorentz and U(1) invari-

ant vector ﬁelds A

,asdiscussedin[13,20]. Any breaking

of the Lorentz or U(1) invariance (by the constraint over the

vector ﬁeld) is understood as spontaneous, hence the stan-

dard Maxwell kinetic terms for the vector ﬁeld, which from

a string perspective is a constraint gauge ﬁeld in a gauged

ﬁxed setting. This stems from the fact that in our world-sheet

logarithmic conformal ﬁeld theory to D-particle recoil [33],

the recoil is described in terms of appropriate open-string

world-sheet vertex operators of the vector ﬁeld A

(cf. (2.6)

below) which are invariant under a U(1) gauge transforma-

tion of A

in target space by construction, A

→ A

+∂

θ.

Details are given in [13,20].

We consider constant dilaton ﬁelds φ = φ

in the galactic

era and weak recoil ﬁelds

√



 1 (appropriate for late

eras of the universe), in which case the above action is well

approximated by (in the Einstein frame with respect to the

dilaton φ)[13]

eff 4D



√

−g



αe

−2φ

μν



R − 

−

G

μν



−

μν

+ λ







+ S

, (2.2)

with

α = α



, J ≡

(2πα



)

3φ

≡

16π G

α T



≡

3φ

 e

2φ

. (2.3)

The tilded vector ﬁeld

in the action (2.2), as compared

to the original action (2.1), results from an appropriate nor-

malisation so that the vector ﬁeld appears with a canonical

(Maxwell) term for its ﬁeld strength

μν

. The quantity λ is

a Lagrange multiplier ﬁeld implementing the constraint on

the recoil-velocity ﬁeld stemming from its interpretation as

a velocity four-vector ﬁeld [20],

= 2.4 × 10

GeV

is the reduced Planck mass in four space-time dimensions

(on our brane universe),

 is a bulk cosmological constant,

which can be constrained (cf. discussion below Eq. (2.4))

by means of the dilaton equation of motion, T

> 0isthe

three-brane universe tension, α



= M

−2

is the Regge slope,

with M

the string scale, and g

the string coupling. For

the rest of this work we assume the phenomenological value

/(4π) = 1/20, that is, g

∼ 0.8, for which string pertur-

bation theory is valid. Moreover, the reader should recall [13]

that, under the assumptions that

μν

is almost constant

and α R  M

, which are appropriate for late eras of the

universe we are interested in here, the dilaton equation of

motion in the action (2.2) leads to an expression of

 in

terms of the brane tension T

, which can be used to obtain



−

3φ

< 0. (2.4)

This anti-de Sitter type cosmological constant would not be

phenomenologically acceptable in the current era, as it would

defy the Cosmic Microwave Background (CMB), Baryon

Acoustic Oscillation (BAO) and gravitational lensing data.

To remedy this fact we assume [13] that contributions from

bulk ﬂux gauge ﬁelds G

μν

(which condense) and distant (to

the brane) D-particles amount to a positive cosmological-

constant type vacuum-energy contribution that ﬁne tunes the

negative cosmological constant (2.4) to an acceptably small

positive amount in the current era. This assumption will be

understood in what follows in the sense that



vac

≡ 

G

μν

+···> 0, (2.5)

where ··· denote other bulk D-particle contributions to the

brane vacuum energy, so that 

vac

is compatible with the

bounds on the cosmological constant  from observations in

For completeness we remark that the vector ﬁeld is expressed in terms

of the recoil four velocity as [13,20]

√



μν

(t)u

where g

μν

(t) = C(η(t))η

μν

is the background cosmological FLRW

metric, with η(t) the conformal time, and C(η) = a

(t) as standard.

In this background the velocity ﬁeld satisﬁes the standard constraint

μν

=−1, which implies the constraint A

μν

=−



. Upon

appropriately normalising the Maxwell kinetic term in the action (2.1),

by redeﬁning the vector ﬁeld as

→



(2πα



)

3φ

one obtains a canonical Maxwell term for the ﬁeld

and the pertinent

constraint implemented by the Lagrange multiplier ﬁeld λ as given in

(2.2). For details we refer the reader to [13,20].

123

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