引力波揭示宇宙弦能量上限：LIGO与未来探测器的约束

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引力波观测对宇宙弦的新限制是近期物理领域的一个重要研究进展，发表于《物理评论快报》(Physics Letters B)第778期(2018年)。该研究论文由Jose J. Blanco-Pillado、Ken D. Olum、Xavier Siemens等学者合作完成，他们在理论物理学领域，特别是宇宙弦和引力波的研究方面有所专长。宇宙弦是一种理论上推测的亚原子尺度的线状结构，它们在早期宇宙的极端条件下可能会形成，并在宇宙中留下独特的引力效应。文章的核心内容聚焦于利用引力波探测技术来限制宇宙弦的存在。作者们对宇宙弦预期产生的随机引力波背景进行了深入分析，并将其结果与脉冲星时序阵列(PTA)的最新观测数据相结合。PTA是通过监测多个脉冲星的射电波信号来探测微弱的引力波信号，如来自宇宙大尺度结构的引力波背景。通过这种结合，研究人员得出了一个重要的科学结论：宇宙弦网络的能量尺度在95%的置信水平下被限制为Gμ < 1.5×10^-11。这里的Gμ是描述宇宙弦张力与普朗克常数的比例，它是衡量宇宙弦强度的重要参数。这一限制意味着如果宇宙弦确实存在，它们的强度必须非常微弱，否则它们应已通过引力波的观测数据被明显地检测到。此外，论文还提到了LIGO（激光干涉引力波天文台）的现有界限，这是一个地面实验，专门用于直接探测强引力波事件。同时，它还预测了未来空间引力波探测器，如LISA（激光干涉空间天线）和BBO（巴布科克引力波天文台）可能达到的限制。这些先进的引力波探测技术将有望进一步提高对宇宙弦的敏感度，从而提供更精确的限制或发现证据。这项研究不仅对宇宙弦理论的发展产生了重要影响，也展示了引力波作为探测宇宙新物理现象的强大工具。随着引力波观测技术的不断进步，宇宙弦这样的理论模型将会面临更为严格的检验，帮助科学家们理解宇宙早期的极端条件和可能的未知物理过程。

Physics Letters B 778 (2018) 392–396

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

New limits on cosmic strings from gravitational wave observation

Jose J. Blanco-Pillado

a,b

, Ken D. Olum

c,∗

, Xavier Siemens

Department of Theoretical Physics, University of the Basque Country, Bilbao, Spain

IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain

Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA

Center for Gravitation, Cosmology, and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA

a r t i c l e i n f o a b s t r a c t

Article history:

Received

8 December 2017

Received

in revised form 18 January 2018

Accepted

18 January 2018

Available

online 31 January 2018

Editor:

M. Trodden

Keywords:

Cosmic

strings

Gravitational

waves

We combine new analysis of the stochastic gravitational wave background to be expected from cosmic

strings with the latest pulsar timing array (PTA) limits to give an upper bound on the energy scale of

the possible cosmic string network, Gμ < 1.5 ×10

−11

at the 95% conﬁdence level. We also show bounds

from LIGO and to be expected from LISA and BBO.

Current

estimates for the gravitational wave background from supermassive black hole binaries are at the

level where a PTA detection is expected. But if PTAs do observe a background soon, it will be diﬃcult in

the short term to distinguish black holes from cosmic strings as the source, because the spectral indices

from the two sources happen to be quite similar.

PTAs do not observe a background, then the limits on Gμ will improve somewhat, but a string network

with Gμ substantially below 10

−11

will produce gravitational waves primarily at frequencies too high for

PTA observation, so signiﬁcant further progress will depend on intermediate-frequency observatories such

as LISA, DECIGO and BBO.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Our universe may contain a network of cosmic strings arising

as topological defects in uniﬁed ﬁeld theories or as fundamental

strings (or 1-dimensional D-branes) in string theory [1–3]. If so,

the best hope for detecting this network is the observation of grav-

itational

waves from oscillating string loops. Correspondingly, the

strongest limits on such a network arise from non-observation of

such gravitational waves.

Gravitation

wave observations may detect a cosmic string

network either through bursts of radiation emitted at cusps or

through the stochastic background composed of radiation from all

loops existing through cosmic history. Bursts were discussed in

Refs. [4–7]; here we will concentrate on the stochastic background.

Current

work [8] has advanced our understanding of the ex-

pected

gravitational wave background spectrum, taking into ac-

count

all known effects, except that Ref. [8] approximated grav-

Corresponding author.

E-mail

addresses: josejuan.blanco@ehu.es (J.J. Blanco-Pillado),

kdo@cosmos.phy.tufts.edu (K.D. Olum), siemens@gravity.phys.uwm.edu

(X. Siemens).

itational back reaction as a smoothing process (implemented by

convolving the string shape with a Lorentzian) instead of calculat-

ing

the exact back-reaction effect on each loop. It is thus appro-

priate

to update existing observational bounds [9–15] on cosmic

string network properties.

Cosmic

strings are classiﬁed by their tension or energy per unit

length μ. The gravitational effects of strings depend on the prod-

uct

Gμ, where G is Newton’s constant. We will work in units

where c = 1, so Gμ is a dimensionless number. Early models of

strings considered Gμ ∼ 10

−6

, which is what one might expect

for symmetry breaking at the grand uniﬁcation scale. At such val-

ues,

strings could be the cause of structure formation, but they

were ruled out long ago as a primary source of large scale struc-

ture

perturbations in the universe by cosmic microwave back-

ground

(CMB) observations. Current limits from CMB observations

give Gμ  10

−7

[16], but pulsar timing observations give a much

stronger limit, as we will discuss.

consider here the usual model of local strings, with no cou-

plings

to any light particle except the graviton. At any given time

the cosmic string “network” consists of inﬁnite strings and a distri-

bution

of loops of various sizes. Loops are formed by reconnection

of long strings with themselves. They oscillate relativistically and

eventually lose their energy to gravitational radiation.

https://doi.org/10.1016/j.physletb.2018.01.050

0370-2693/

SCOAP

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