The Dust Between the Stars

I · The claim at full strength

An excess, and a model that fits it

BICEP2 watched one patch of southern sky, about 380 square degrees, at 150 GHz, for three seasons from 2010 to 2012. What it measured is polarisation. The cosmic microwave background, the oldest light there is, is slightly polarised, and the pattern of that polarisation across the sky splits into two kinds. E-modes, arranged like spokes or rings, are made by ordinary ripples in density. B-modes, curls with a handedness, are not. Gravitational waves from inflation would make B-modes. So does gravitational lensing, which twists some E-mode pattern into B-mode on its way to us, by an amount that can be calculated. And so does dust: grains in our own galaxy, lined up by its magnetic field, glowing in polarised light.

The team found more B-mode power than lensing predicts, between multipoles 30 and 150 (angular scales of a few degrees down to about one), and fitted it with lensing plus primordial tensor modes, whose strength is the tensor-to-scalar ratio r. Their abstract states the result like this:

The observed B-mode power spectrum is well fit by a lensed-ΛCDM + tensor theoretical model with tensor-to-scalar ratio r=0.20^+0.07_−0.05, with r=0 disfavored at 7.0σ.

BICEP2 Collaboration, abstract, Physical Review Letters (2014)

Two things belong right beside that sentence, because the authors put them there. The fit has no foreground subtraction in it: no dust. And the same abstract says of the dust models that were available to them:

However, these models are not sufficiently constrained by external public data to exclude the possibility of dust emission bright enough to explain the entire excess signal.

They had tested the frequency dependence with what they had, a map from the earlier BICEP1 telescope at 100 GHz:

Cross correlating BICEP2 against 100 GHz maps from the BICEP1 experiment, the excess signal is confirmed with 3σ significance and its spectral index is found to be consistent with that of the CMB, disfavoring dust at 1.7σ.

and the published version ends its abstract with a sentence the following year would test:

Accounting for the contribution of foreground dust will shift this value downward by an amount which will be better constrained with upcoming datasets.

arXiv:1403.3985v3, abstract

That caveat was not in the March preprint, which said instead: “We also estimate potential foreground signals and find that available models predict these to be considerably smaller than the observed signal.” It gave the BICEP1 cross-check as “disfavoring synchrotron or dust at 2.3σ and 2.2σ, respectively”, and it ended:

Subtracting the best available estimate for foreground dust modifies the likelihood slightly so that r=0 is disfavored at 5.9σ.

arXiv:1403.3985v1, abstract (17 March 2014)

The published version dropped the dust model behind that estimate. A footnote says why: “In the preprint version of this paper an additional DDM2 model was included based on information taken from Planck conference talks.” In its place came the caveat above. The headline, r = 0.20 +0.07 −0.05 with r = 0 disfavoured at 7.0σ, is the same in both versions, and it is the headline this page reproduces.

The claim, recomputed from their own numbers

The collaboration released its likelihood for r as a table, the black curve of the middle panel of their Figure 10: 751 values of r from 0 to 0.75. The page reads that table and summarises it with the one function it uses for every curve on this page: find the peak, integrate the curve as straight segments, and find the height at which the region above it holds 68% of the area, which is how the paper defines its interval.

The button runs the 2015 likelihood at 220,248 points in your browser: a few seconds on a laptop, longer on a phone.

The recomputed peak is 0.196, with a 68% interval from 0.145 to 0.262, so the errors about the peak are −0.051 and +0.066. Rounded as the paper rounds, that is r = 0.20 +0.07 −0.05. The height of the curve at r = 0, as a fraction of its peak, is 3.05 × 10⁻¹¹; converted the way the paper converts it, √(−2 ln ratio) = 6.96, which rounds to the printed 7.0σ. Two small differences are printed rather than hidden: Section XI.1 gives the ratio as 2.9 × 10⁻¹¹, not the released table's 3.05 × 10⁻¹¹, and its probability to exceed as 3.3 × 10⁻¹², where the released table, converted the same way, gives 3.4 × 10⁻¹². The claim comes back at the strength it was printed.

Two numbers in that abstract are easy to confuse. The 7.0σ is the rejection of r = 0 inside a model with no dust in it. It is not a 7.0σ rejection of dust. The abstract's other figure, an excess at more than 5σ, is the excess over lensing alone. Neither was ever a measurement of where the excess came from.

II · The deciding control

The same patch of sky, at a frequency where dust is loud

One thing tells primordial B-modes from dust, and it cannot be seen at a single frequency: how each changes with frequency. In the temperature units cosmologists use for the microwave background, the background is equally bright at every frequency; that is what the units are built to do. Dust is not. Its grains glow like a cold body at about 19.6 kelvin whose emission peaks at far higher frequencies, so on the way up from 150 GHz it brightens steeply.

Integrated over the real bandpasses, the dust amplitude in each map relative to a nominal 353 GHz is 0.0446 for BK150, 0.1443 for Planck's 217 GHz map and 1.1301 for its 353 GHz map. In amplitude, dust is 25.4 times brighter at 353 GHz than at 150. The joint paper puts it in words:

…dust emission is approximately 25 times brighter in the Planck 353 GHz band than it is in the BICEP2/Keck 150 GHz band (integrating appropriately over the instrumental bandpasses).

BICEP2/Keck and Planck Collaborations, Section II.3

Planck posted its measurement of polarised dust away from the galactic plane in September 2014, with an extrapolation into the BICEP2 field. The abstract of the accepted version, revised that December, ends:

This is the same magnitude as reported by BICEP2 over this ℓ range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.

Planck intermediate results XXX, abstract of arXiv:1409.5738v2

So the two teams did the decisive thing together. BICEP2 and the Keck Array, a set of BICEP2-like receivers that watched the same field at the same frequency during the 2012 and 2013 seasons, supplied a deeper 150 GHz map, called BK150 here. Planck supplied its maps at 217 and 353 GHz. Between three maps there are six spectra, three autos and three crosses, and all six enter one likelihood. The cross between BK150 and 353 GHz is the sharpest question on the page: does the pattern BICEP2 saw appear in a map made where dust is 25.4 times brighter?

Moving from the gold curve to the blue one changes two things at once: the data (a deeper 150 GHz map, plus Planck) and the model (dust is now a parameter). It is not one switch thrown on the 2014 data.

The 2015 likelihood, rerun here

For each of five bins in multipole the page builds the 3 × 3 matrix of measured power between the three maps and compares it with the model's matrix through the nonlinear transform of Hamimeche and Lewis, which is what the paper used. It then weighs all thirty numbers, five bins of six spectra, with the released covariance, every correlation between them included. The model holds lensing at its expected level and has three parameters: r, free on [0, 0.5]; a dust amplitude A_d, free on [0, 15] μK², defined at multipole 80 and 353 GHz; and the dust spectral index β_d, with the paper's Gaussian prior of 1.59 ± 0.11. Dust amplitude and index are integrated out on a grid, leaving a curve for r alone.

When this page was built, the same engine ran this rerun, and the verifier re-checks every figure in this paragraph; the button above recomputes them in your browser. The rerun lands where the paper did. Its peak is at r = 0.048 against the printed 0.048. Its 95% upper endpoint is 0.121, against the printed r < 0.12. The likelihood at r = 0 is 0.372 of its peak, against the printed 0.38, and the paper's conversion turns that into a chance of 8.0% of a ratio so small if r were truly zero (printed: 8%). The dust amplitude peaks at 3.2 μK² against the printed 3.3, and zero dust is disfavoured at 5.13σ against the printed 5.1σ. Every gap and tolerance is in the check below.

We find strong evidence for dust and no statistically significant evidence for tensor modes.

BICEP2/Keck and Planck Collaborations, abstract, Physical Review Letters (2015)

The BICEP2 collaboration is an author of that analysis. It is their own reply, made with more data, and it is the reply the page reruns. The same abstract adds a sentence with a coincidence in it:

Marginalizing over dust and r, lensing B-modes are detected at 7.0σ significance.

Same number as 2014, different question. In 2014 the 7.0σ rejected r = 0 in a model without dust. In 2015 the 7.0σ is the lensing, measured with dust and r both integrated out. The excess BICEP2 found was real. What changed was the account of what made it.

III · Fit it yourself

Six spectra, three knobs

Before a grid is summarised into a curve, here is what it is summarising. Each panel below is one of the six spectra: measured points in blue, with their diagonal errors. The bars are the model at your settings, stacked: lensing in grey, primordial tensor modes in gold, dust in rust. Every setting is scored by the same 2015 likelihood the grid uses, thirty bandpowers and all their correlations at once, and the score is printed as a chi-square: lower is better.

Under each panel: the sum over its five bins of (data − model)² / error², with diagonal errors only. It is a reading aid that ignores correlations; the chi-square above is the likelihood.

Start from the 2014 model. BK150 × BK150, the 150 GHz auto-spectrum, the kind BICEP2 alone measured in 2014, is fitted tolerably. Now look at BK150 × 353. The model predicts almost nothing there, because the microwave background and lensing are small, while the measured cross-power in the first bin is 0.167 μK². Raise A_d and that panel fills. The dust it takes to do so also lands on BK150 × BK150, scaled down by the frequency law, and r has to come down to make room. The whole argument of 2015 is in that trade.

In numbers: the 2014 model scores a chi-square of 72.4 on the thirty bandpowers, and the best point on the joint grid (r = 0.048, A_d = 3.2 μK², β_d = 1.59) scores 45.3 including its prior penalty, a difference of 27.1. At the paper's own grid maximum (r = 0.05, A_d = 3.30, β_d = 1.6) the page's chi-square is 45.3; the paper reports 40.8 for 28 degrees of freedom there, computed by recomputing the bandpower covariance for that model rather than with the approximation used in the fit. Those are different statistics, and the page does not claim to reproduce the second.

IV · The control on the control

Could this test have said yes?

A test that finds nothing is only as strong as its ability to find something. So take the 2015 data, add exactly what r = 0.2 would have added, and run the unchanged analysis.

Grade A: the claimed effect, at the claimed size, planted into the control's own data.

The operation, named plainly: add the expected tensor bandpowers to this observed sky.

The addition is not a curve drawn over the result. For each of the six spectra and five bins, the page takes the collaboration's own 2014 theory spectrum for tensor modes alone at r = 0.1, passes it through that spectrum's released bandpower window, doubles it to r = 0.2, and adds it to the measured value. In this release the six windows within each bin are identical, so every spectrum in a bin receives the same added power, as the table of added bandpowers below shows. The microwave background is one sky seen by all three maps, so every auto and every cross spectrum receives it. Nothing else moves: the noise, the fiducial model, the covariance, the priors and the algorithm are the ones that produced the blue curve.

·

When this page was built, the same engine ran the plant, and the verifier re-checks what follows; the button recomputes it here. Planted at r = 0.2, the peak moves from 0.048 to 0.248: a rise of 0.200. The planted curve's 68% interval runs from 0.191 to 0.309. The profile statistic goes from 1.34 to 5.05. The rule was a rise within 0.02 of 0.20 and a profile statistic of at least 3. It was declared in the page's specification, whose independent pilot had already run this default setting; the builder did not change it. Verdict on this sky: RECOVERED.

The two halves of the rule do different jobs. A plant shaped exactly like the model should raise the peak by about the planted amount whatever the noise, so the rise is a check for bias, not for power. The profile statistic is the half that measures power. The specification gives no derivation for either threshold; this page reads 0.02 as a tenth of the planted size (five steps of the r grid), and 3 as a descriptive bar well above the measured sky's value, not a calibrated probability. To show that the power half can say no, the verifier runs the same plant through the same likelihood on a copy of the data with every bandpower error doubled (the covariance scales; the noise offsets are left alone, so this is a test of the rule, not a model of a real noisier experiment). The rise is then 0.196, the profile statistic reaches only 2.81, and the rule returns INCONCLUSIVE.

Notice that the peak does not land on 0.2. It lands near a quarter, because the measured sky already leaned a little above zero, and adding a signal does not remove what was there. Forcing the answer to come back as exactly 0.2 would hide the operation actually performed.

The injection a hurried recipe would write

Add the signal to five of the spectra and forget 217 × 353, and the result is not a sky at all. Arrange the added power as a matrix between the three maps: any real added signal makes that matrix positive semidefinite, and with one cross missing its smallest eigenvalue is 1 − √2 = −0.414 times the added power. The engine does not test that eigenvalue. It checks that every auto and cross spectrum received exactly its windowed share of the common sky, finds that 217 × 353 did not, and refuses the input rather than fitting it; the eigenvalue is why that check is needed.

What this does and does not show

One observed sky is held fixed and the expected tensor power is added to it. No new sky is simulated, no chance correlation between the planted signal and the dust or the noise is drawn, and nothing here is a percentage of repeated experiments that would succeed. It shows that this analysis, on these data, responds to a signal of the claimed size in the way a detection needs. The collaboration's own simulations bear on the ensemble question only indirectly: in lensed-ΛCDM plus noise plus dust simulations with no tensor signal, the median 95% upper limit was r < 0.075, far below 0.2 (printed in the joint paper, not recomputed here).

V · The second layer

How much does the dust prior decide?

The one assumption the 2015 fit cannot do without is the dust spectral index. The cross spectra alone cannot pin β_d down, so the paper imposed a Gaussian prior of 1.59 ± 0.11, taken from Planck's measurements of other parts of the sky. An assumption like that can hide a claim in either direction: a steeper dust law makes the 353 GHz dust smaller at 150 GHz and leaves more room for r; a shallower one does the reverse. The paper moved the prior centre and printed where the peak went. Here you can move it too, drop the 217 GHz map entirely, and see the part the paper did not print: whether a planted r = 0.2 still comes back under each choice.

Runs when you press Run or change a choice; the first run of a map selection builds its grid.

The page's result. Each row runs the same unchanged likelihood on the measured sky and on the same sky with r = 0.2 added, at one prior centre and one complete map selection. The paper printed peaks only for its own map selection.

The paper printed peaks of r = 0.021 for a prior centred on 1.3 and r = 0.073 for 1.9. The rerun gives 0.020 and 0.072, each within one step of its r grid (0.004) of the printed value.

This page's result, computed when the page was built and re-checked by its verifier. 6 of 6 paired settings meet the declared recovery rule. Without the plant, the 95% upper endpoint ranges from 0.103 to 0.143; with r = 0.2 added, the fitted peak rises by 0.184 to 0.208 and the profile statistic reaches 3.51 to 6.47. The closest call is BK150 + 353 GHz with the prior centred on 1.30: its rise of 0.184 is 0.004 inside the rule's edge. The dust prior moves where the measured sky's curve peaks, exactly as the paper said, and it moves the upper limit; it does not take away the analysis's ability to see a signal of the size claimed in 2014.

Novelty, bounded: we searched NASA LAMBDA, GitHub and Observable on 2026-09-22 and did not find a reader-facing page that combines the original BICEP2 likelihood with a live joint HL control and a coherent r = 0.2 injection while exposing dust-prior sensitivity. The paper itself explored these priors and map subsets (Section III.3), and the released likelihood and CosmoMC are the computational precedents. What is added here is the paired, reproducible recovery calculation on the released observed vector.

VII · The scientific record

What the record decided

The verdict is narrow on purpose. Its subject is the attribution of the 2014 excess to primordial gravitational waves near r = 0.2. The excess itself was real; lensing, measured underneath it, was detected at 7.0σ in the joint analysis; and the lensed-ΛCDM + tensor fit with no dust is reproducible under its stated assumptions, as section I shows. The verdict says nothing against inflation, or against primordial gravitational waves at some smaller amplitude. The collaboration revised its own account, with a deeper 150 GHz map and Planck's higher frequencies, and published the revision jointly with Planck.

What this page adds, computed when it was built and re-checked by its verifier. Recomputed here, the 2014 likelihood peaks at r = 0.196 with r = 0 disfavoured at 6.96σ; the 2015 joint likelihood peaks at r = 0.048 with a 95% upper endpoint of 0.121; and r = 0.2 added to the 2015 data raises its peak by 0.200, with a profile statistic of 5.05, so this control could have confirmed the claim on this observed sky.

How it went

1. 17 March 2014 BICEP2 posts its result (arXiv:1403.3985v1).
2. 22 May 2014 Mortonson and Seljak post a joint BICEP2 and Planck analysis that assumes nothing about the dust polarisation but its power spectrum shape (arXiv:1405.5857v1).
3. 28 May 2014 Flauger, Hill and Spergel post a reanalysis of the foregrounds in the BICEP2 region (arXiv:1405.7351v1).
4. 19 June 2014 The BICEP2 paper is published in Physical Review Letters, with the dust caveat in its abstract.
5. 19 September 2014 Planck posts its measurement of polarised dust at high Galactic latitude, including the BICEP2 field (arXiv:1409.5738v1).
6. 2 February 2015 BICEP2/Keck and Planck post their joint analysis (arXiv:1502.00612v1).
7. 9 March 2015 The joint analysis is published in Physical Review Letters.
8. 1 October 2021 BICEP/Keck post BK18, with an upper limit of r < 0.036 at 95% confidence (arXiv:2110.00483v1).
9. 25 February 2026 BICEP/Keck XX, component-separated maps, is published in the Astrophysical Journal.
10. 27 August 2026 A BICEP Array status paper, revised this day, still names BK18 as the latest published result and says a BK24 manuscript is in preparation (arXiv:2608.25015v2).

Since then

With BICEP3 and more Keck Array frequencies through the 2018 season, the collaboration's own foreground model no longer needs the external dust prior at all, and its limit is r_0.05 < 0.036 at 95% confidence. That is a published result, not a calculation on this page, and it is not the tightest limit from every combination of data: combining it with Planck and baryon acoustic oscillations gives r < 0.032. In 2026 a component-separated map analysis of the same observations found 84% correlation with the baseline pipeline; that is a second analysis of overlapping data, not an independent observing campaign and not a new detection. The latest status report this page found, a BICEP Array paper revised on 27 August 2026, still says “The latest published result from the BICEP program consists of all BICEP data from 2010 through 2018 as well as external data from WMAP and Planck (BK18)”, and that “a complete BK24 manuscript is currently in preparation.” Its preliminary BK24 maps are not a new limit. A July 2026 conference abstract that the specification read says the same; this build could not reopen it. Together they bound the status search behind this date.

What would change it

An independently supported foreground separation that establishes a primordial component of the original claimed size, and explains its disagreement with the later multifrequency constraints, would change this verdict. A future detection of a much smaller r would advance the search for primordial gravitational waves without retrospectively establishing the 2014 attribution near r = 0.2.

Sources

1. BICEP2 Collaboration, P. A. R. Ade et al. (2014). Detection of B-Mode Polarization at Degree Angular Scales by BICEP2. Physical Review Letters 112, 241101. Published 19 June 2014. DOI 10.1103/PhysRevLett.112.241101. Preprint arXiv:1403.3985v3, revised 23 June 2014.
2. BICEP2/Keck and Planck Collaborations, P. A. R. Ade et al. (2015). Joint Analysis of BICEP2/Keck Array and Planck Data. Physical Review Letters 114, 101301. Published 9 March 2015. DOI 10.1103/PhysRevLett.114.101301. Preprint arXiv:1502.00612v2, revised 14 April 2015.
3. BICEP/Keck Collaboration, P. A. R. Ade et al. (2021). Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season. Physical Review Letters 127, 151301. Published 4 October 2021. DOI 10.1103/PhysRevLett.127.151301. Preprint arXiv:2110.00483v1, 1 October 2021.
4. BICEP/Keck Collaboration, P. A. R. Ade et al. (2026). BICEP/Keck. XX. Component-separated Maps of the Polarized Cosmic Microwave Background and Thermal Dust Emission Using Planck and BICEP/Keck Observations through the 2018 Observing Season. Astrophysical Journal 999(1), 89. Published 25 February 2026. DOI 10.3847/1538-4357/ae3e53. Preprint arXiv:2509.21648v2, revised 29 January 2026.
5. Planck Collaboration, R. Adam et al. (2016). Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes. Astronomy and Astrophysics 586, A133. DOI 10.1051/0004-6361/201425034. Preprint arXiv:1409.5738v1, 19 September 2014; accepted version arXiv:1409.5738v2, 8 December 2014, whose abstract is quoted.
6. A. Steiger et al. (2026). Status of BICEP Array and Integration of the 220/270 GHz Receiver. Preprint arXiv:2608.25015v2, revised 27 August 2026. A status report with preliminary maps, not a new limit.
7. M. Tristram et al. (2022). Improved limits on the tensor-to-scalar ratio using BICEP and Planck data. Physical Review D 105, 083524. Published 26 April 2022. DOI 10.1103/PhysRevD.105.083524. Preprint arXiv:2112.07961.
8. M. J. Mortonson and U. Seljak (2014). A joint analysis of Planck and BICEP2 B modes including dust polarization uncertainty. Journal of Cosmology and Astroparticle Physics 10 (2014) 035. Preprint arXiv:1405.5857v1, 22 May 2014.
9. R. Flauger, J. C. Hill and D. N. Spergel (2014). Toward an Understanding of Foreground Emission in the BICEP2 Region. Preprint arXiv:1405.7351v1, 28 May 2014.
10. B. Singari (2026). Advancing Constraints on Primordial Gravitational Waves with BICEP. Division of Particles and Fields 2026, Fermilab, 21 July 2026. Conference abstract, not a peer-reviewed limit; read for the specification, and not reopened by this build (HTTP 403).
11. S. Hamimeche and A. Lewis (2008). Likelihood analysis of CMB temperature and polarization power spectra. Physical Review D 77, 103013. Preprint arXiv:0801.0554.